132. A body moving through air at high speed ‘v’ experiences a retarding force given by f = k A vx, where A is the surface area of the body, is density of air and k is dimensionless constant. Deduce the expression.
133. The position of a particle moving along on X – axis is given by x = A t2 + Bt + C. The numerical value of A, B and C are 1, -4, 2. Find (i) dimension of A, B and C, (ii) the velocity of the particle at t = 4 sec, (iii) acceleration of the particle when t = 4 sec, (iv) the average velocity during the interval t = 0 to t = 5 sec.
134. A stone is dropped from a balloon going up with a velocity 5 m / s. If the balloon was 50m high when a stone was dropped, find its height when the stone hits the ground. [ 68.5 m]
135. A football is kicked horizontally with uniform velocity towards a vertical wall. If the ball rebound after colliding at the wall with same velocity, draw (i) speed – time (ii) velocity – time curve.
133. The position of a particle moving along on X – axis is given by x = A t2 + Bt + C. The numerical value of A, B and C are 1, -4, 2. Find (i) dimension of A, B and C, (ii) the velocity of the particle at t = 4 sec, (iii) acceleration of the particle when t = 4 sec, (iv) the average velocity during the interval t = 0 to t = 5 sec.
134. A stone is dropped from a balloon going up with a velocity 5 m / s. If the balloon was 50m high when a stone was dropped, find its height when the stone hits the ground. [ 68.5 m]
135. A football is kicked horizontally with uniform velocity towards a vertical wall. If the ball rebound after colliding at the wall with same velocity, draw (i) speed – time (ii) velocity – time curve.
136. Human body can survive a negative acceleration trauma incident if the magnitude of acceleration is less than 250 m/s2. If you are in automobile accident with a initial speed 105 km/hr and are stopped by an airbag that inflates from the dash-board, over what distance must the air bag stop you to survive the crash ?
[ 1.7 m ]
137. A canoe has velocity of 0.40 m/south-east relative to the earth. The canoe is on the river that is flowing 0.50 m/s east relative to the earth. Find the velocity of the canoe relative to the river. [ 0.354m/s, -52.50, south of west ]
138. A 8 kg ice block, released from the top of a 1.5 m long frictionless ramp, sliding downhill, reaching a speed of 2.5 m/s at the bottom. What is the angle between the ramp and the horizontal? If the coefficient of friction is 0.05, what is the new angle of inclination?
[ 1.7 m ]
137. A canoe has velocity of 0.40 m/south-east relative to the earth. The canoe is on the river that is flowing 0.50 m/s east relative to the earth. Find the velocity of the canoe relative to the river. [ 0.354m/s, -52.50, south of west ]
138. A 8 kg ice block, released from the top of a 1.5 m long frictionless ramp, sliding downhill, reaching a speed of 2.5 m/s at the bottom. What is the angle between the ramp and the horizontal? If the coefficient of friction is 0.05, what is the new angle of inclination?
139. Thorium decays by the emission of alpha particle ( A = 4 ) to an isotopes of Radium ( A = 226 ). Calculate the ratio of the speed of the alpha particle to the radium and hence calculate recoil KE of the Radium if the ejected energy of the alpha particle is 4.6 MeV.
[113:2, 0.082 MeV]
[113:2, 0.082 MeV]
140. A man of mass 70 kg is standing on a large sheet of frictionless ice and holding a large rock of mass 15 kg. In order to get off the ice, the man throws the rock at speed 12 m/s relative to earth at an angle 350 above the horizontal. What is his initial speed after he throw the rock ? [ 2.11 m/s]
141. Rain falls vertically onto a plane roof 1.5 m square, which is inclined to the horizontal at an angle of 300. The rain drops strike the roof with a vertical velocity of 3 m/s and a volume of 2.5 x 10-2 m3 of water is collected from the roof in one minute. Assuming that the conditions are steady and the velocity of raindrop after impact is zero, calculate (a) vertical force exerted on the roof by the impact of the rain and (b) pressure normal to the roof due to the impact of the of the rain. (c) If, instead, the roof were subject to a rain of hard spheres, which collided elastically, what would be the normal pressure on the roof then be? ( Density of water 1000 kg/m3) [1.25N, 0.48N/m2, 0.96Pa]
142. A fire engine pumps water at such a rate that the velocity of the water leaving the nozzle is 15 m/s. If the jet be directed perpendicularly on to a wall and rebound of the water be neglected, calculate the pressure on the wall. 1 m3 of water has mass 1000 kg. [ 2.25 x 105 N/m2]
143. In a nuclear collision, an alpha particle A of mass 4 unit is incident with velocity v on a stationary helium nucleus B of 4 mass unit. After collision, A moves in the direction BC with velocity v/2, where BC makes angle 600 with initial direction AB and the helium nucleus moves along BD. Calculate the velocity of rebound of the helium nucleus along BD and angle made with the direction AB. [ 0.87v, 300 ]
144. The diagram shows identical simple pendulums of length 0.8m . Bob A is raised with the string taut to the horizontal position A’ and released. Calculate (a) Velocity with which A strikes B. (b) velocities of A and B just after A makes a perfectly elastic collision with B. [ 4m/s, 4m/s]
145. Sand is deposited at rate 20 kg/s in a conveyor belt moving horizontally at 10m/min. Find (i) force required to maintain constant velocity, (ii) Power required to maintain constant velocity, (iii) Rate of change of KE of the sand. [10/3N, 5/9W, 5/18W]
141. Rain falls vertically onto a plane roof 1.5 m square, which is inclined to the horizontal at an angle of 300. The rain drops strike the roof with a vertical velocity of 3 m/s and a volume of 2.5 x 10-2 m3 of water is collected from the roof in one minute. Assuming that the conditions are steady and the velocity of raindrop after impact is zero, calculate (a) vertical force exerted on the roof by the impact of the rain and (b) pressure normal to the roof due to the impact of the of the rain. (c) If, instead, the roof were subject to a rain of hard spheres, which collided elastically, what would be the normal pressure on the roof then be? ( Density of water 1000 kg/m3) [1.25N, 0.48N/m2, 0.96Pa]
142. A fire engine pumps water at such a rate that the velocity of the water leaving the nozzle is 15 m/s. If the jet be directed perpendicularly on to a wall and rebound of the water be neglected, calculate the pressure on the wall. 1 m3 of water has mass 1000 kg. [ 2.25 x 105 N/m2]
143. In a nuclear collision, an alpha particle A of mass 4 unit is incident with velocity v on a stationary helium nucleus B of 4 mass unit. After collision, A moves in the direction BC with velocity v/2, where BC makes angle 600 with initial direction AB and the helium nucleus moves along BD. Calculate the velocity of rebound of the helium nucleus along BD and angle made with the direction AB. [ 0.87v, 300 ]
144. The diagram shows identical simple pendulums of length 0.8m . Bob A is raised with the string taut to the horizontal position A’ and released. Calculate (a) Velocity with which A strikes B. (b) velocities of A and B just after A makes a perfectly elastic collision with B. [ 4m/s, 4m/s]
145. Sand is deposited at rate 20 kg/s in a conveyor belt moving horizontally at 10m/min. Find (i) force required to maintain constant velocity, (ii) Power required to maintain constant velocity, (iii) Rate of change of KE of the sand. [10/3N, 5/9W, 5/18W]
146. Calculate the acceleration and tension in each case.
147. If coefficient of friction is 0.1, determine new acceleration in each case.
148. A bullet of mass 0.01 kg moving with velocity 500 m / s strikes a block of mass 2 kg which is suspended by a string of length 5 m. If the block rises the vertical height 0.1 m , calculate the emergent velocity of the bullet. [ 220 m/s]
149. According to ‘Chandrasekhar limit’ burnt-out star of size three times the solar mass undergoes into black hole. What is the radius of the event horizon?
150. Mass of sun is 330000 times greater than that of earth. For a person at the surface of earth, the average distance from the center of sun is 23500 times the distance to the center of the earth. What is the ratio of the sun’s gravitational force to that of earth’s?
151. Two people are carrying a uniform wooden board that is 3m long and weighs 160 N. If one person applies an upward force equal to 600 N at one end, at what point does the other person lift?
152. A mass X of 0.1 kg is attached to the free end of a vertical helical spring whose upper end is fixed and the spring is extended to 0.04m. X is now pulled down to 0.02 m and then released. Find its (i) Period, (ii) Maximum force during oscillation, (iii) Maximum KE. [0.4 sec, 0.5 N, 0.005 J]
153. A solid body floats with one-half of its volume outside the water and floats 3/8 of its volume outside in another liquid. What is the density of solid and liquid?
[ 0.5 and 0.8 g /cc ]
154. A disc of moment of inertia 0.1 kg m2 about its center and radius 0.2 m is released from rest on a plane inclined at 300 to the horizon. Calculate angular velocity after it has rolled 2m down the plane if its mass is 5 kg. [ 18.3 rad / s ]
155. What is the power output in horse power of an electric motor turning at 4800 rev/min and developing a torque of 4.30 Nm?
156. A braided nylon rope, 2.5 cm in diameter has a breaking strength of 1.24 x 105 N. Find the breaking strength of similar ropes 1.25 cm in diameter.
157. A compressed tank of rocket contains 0.25 m3 of kerosene, with mass 205 kg. The pressure at the top of the kerosene is 2.01 x 105 Pa. The kerosene exerts a force 16.4 N at the bottom of the tank, which has area 0.07 m2. Find the depth of the kerosene.
158. A soap bubble of in a vacuum has a radius 3 cm and another at vacuum has 6 cm. If the two bubbles coalesce under isothermal condition, calculate the radius of the formed bubble.
159. Water flows steadily along a uniform tube of cross-section 30 cm2. The static pressure is 1.2 x 105 Pa and the total pressure is 1.28 x 105 Pa. Calculate the flow velocity and the mass of the water per second flowing.
Revision
HSEB Exam Questions
149. According to ‘Chandrasekhar limit’ burnt-out star of size three times the solar mass undergoes into black hole. What is the radius of the event horizon?
150. Mass of sun is 330000 times greater than that of earth. For a person at the surface of earth, the average distance from the center of sun is 23500 times the distance to the center of the earth. What is the ratio of the sun’s gravitational force to that of earth’s?
151. Two people are carrying a uniform wooden board that is 3m long and weighs 160 N. If one person applies an upward force equal to 600 N at one end, at what point does the other person lift?
152. A mass X of 0.1 kg is attached to the free end of a vertical helical spring whose upper end is fixed and the spring is extended to 0.04m. X is now pulled down to 0.02 m and then released. Find its (i) Period, (ii) Maximum force during oscillation, (iii) Maximum KE. [0.4 sec, 0.5 N, 0.005 J]
153. A solid body floats with one-half of its volume outside the water and floats 3/8 of its volume outside in another liquid. What is the density of solid and liquid?
[ 0.5 and 0.8 g /cc ]
154. A disc of moment of inertia 0.1 kg m2 about its center and radius 0.2 m is released from rest on a plane inclined at 300 to the horizon. Calculate angular velocity after it has rolled 2m down the plane if its mass is 5 kg. [ 18.3 rad / s ]
155. What is the power output in horse power of an electric motor turning at 4800 rev/min and developing a torque of 4.30 Nm?
156. A braided nylon rope, 2.5 cm in diameter has a breaking strength of 1.24 x 105 N. Find the breaking strength of similar ropes 1.25 cm in diameter.
157. A compressed tank of rocket contains 0.25 m3 of kerosene, with mass 205 kg. The pressure at the top of the kerosene is 2.01 x 105 Pa. The kerosene exerts a force 16.4 N at the bottom of the tank, which has area 0.07 m2. Find the depth of the kerosene.
158. A soap bubble of in a vacuum has a radius 3 cm and another at vacuum has 6 cm. If the two bubbles coalesce under isothermal condition, calculate the radius of the formed bubble.
159. Water flows steadily along a uniform tube of cross-section 30 cm2. The static pressure is 1.2 x 105 Pa and the total pressure is 1.28 x 105 Pa. Calculate the flow velocity and the mass of the water per second flowing.
Revision
HSEB Exam Questions
160. A bullet of mass 20gm, moving with velocity 500 m/s passes through a wooden block of mass 100 kg, initially at rest. The bullet emerges out with a speed 100 m/s and the block slides 20 cm. Find coefficient of sliding friction. [ 0.16 ]
161. A ball of mass 4kg moving with a velocity 10 m/s collides with another body of mass 16 kg moving with 4 m/s in opposite direction. If both coalesce into a single body, determine loss of energy on impact. [ 313.6 J ]
162. A ball A of mass 0.1 kg moving with a velocity of 6 m/s collides with B of mass 0.2 kg at rest. Calculate their common velocity if both ball move off together. If A had rebounded with a velocity of 2 m/s, in the opposite direction, what would be the new velocity of B? [ 2m/s, 4m/s ]
163. A bullet of mass 20 g traveling horizontally at 100 m/s embeds in the wooden block of mass 1 kg which is suspended by vertical string of length 1m. Calculate the maximum inclination of the string. [ 36.10 ]
164. A car of mass 2000 kg moves at the speed 20 m/s along a horizontal road where the frictional force is 200 N. Calculate the power developed by the engine. If the car now travels in an inclined road of inclination 150, what will be the new power developed? [4 Kw,107 Kw]
165. A mass of gas emitted from the rear of toy rocket is initially 0.2 kg/s. If the speed of the gas relative to the rocket is 40 m/s, and the mass of the rocket is 4 kg, what is the initial acceleration of the rocket? [ 2 m/s2 ]
161. A ball of mass 4kg moving with a velocity 10 m/s collides with another body of mass 16 kg moving with 4 m/s in opposite direction. If both coalesce into a single body, determine loss of energy on impact. [ 313.6 J ]
162. A ball A of mass 0.1 kg moving with a velocity of 6 m/s collides with B of mass 0.2 kg at rest. Calculate their common velocity if both ball move off together. If A had rebounded with a velocity of 2 m/s, in the opposite direction, what would be the new velocity of B? [ 2m/s, 4m/s ]
163. A bullet of mass 20 g traveling horizontally at 100 m/s embeds in the wooden block of mass 1 kg which is suspended by vertical string of length 1m. Calculate the maximum inclination of the string. [ 36.10 ]
164. A car of mass 2000 kg moves at the speed 20 m/s along a horizontal road where the frictional force is 200 N. Calculate the power developed by the engine. If the car now travels in an inclined road of inclination 150, what will be the new power developed? [4 Kw,107 Kw]
165. A mass of gas emitted from the rear of toy rocket is initially 0.2 kg/s. If the speed of the gas relative to the rocket is 40 m/s, and the mass of the rocket is 4 kg, what is the initial acceleration of the rocket? [ 2 m/s2 ]
166. A disc rolling along a horizontal plane has a moment of inertia 4 kgm2 about its center and mass of 5 kg. The velocity along the plane is 2 m/s and radius is 2m, find (i) angular velocity (ii) total energy of the disc. [ 1rad/s, 12J ]
167. A roller whose diameter is 1m weights 360N. What horizontal force is necessary to pull the roller over the brick 0.1m high when the force is applied at the center? [ 270 N ]
168. A 200 kg satellite is lifted to an orbit of 2.2×104 km radius. If radius and mass of the earth are 6400km and 6 x 1024 kg respectively, how much additional PE is required to lift the satellite? [ 8.87 x 109 J ]
169. The density of ice is 971 kg/m3 and the density of sea water is 1025 kg/m3. What fraction of iceberg is beneath the water surface? [ 0.947 : 1 ]
170. An iceberg having volume 2060 cc floats in sea water of density 1030 kg/m3 with a portion of 224 cc above the surface. Calculate the density of the ice. [ 0.89 g/cc ]
171. A bullet of mass 10g is fired from a gun of mass 1 kg with a velocity of 100 m/s. Calculate the ratio of the KE of the bullet and the gun. [ 100:1]
172. A coin placed on a disc rotates with speed of 331/3 rev/min provided that the coin is not more than 10 cm from the axis. Calculate the coefficient of static friction.
173. Speed of a body spinning about an axis increases from rest to 100 rev/min in 5 sec if a constant of 20 NM is applied. The torque is removed and the body comes to rest 100 sec due to friction. Calculate the frictional torque.
174. A 25 cm thick block of ice floating on fresh water can support a 80 kg man standing on it. What is the smallest area of the ice block? ( Sp gravity of ice = 0.917)
175. A small mass rests on a horizontal platform which vibrates in a SHM with a period of 0.25 s. Find the maximum amplitude of the motion which will allow the mass to remain in contact with platform thought the motion.
176. Calculate the period of the revolution of the satellite revolving at a distance of 20 km from the earth surface. ( R = 6400km, g = 10 m/s2 ) [ 5050.13 s ]
167. A roller whose diameter is 1m weights 360N. What horizontal force is necessary to pull the roller over the brick 0.1m high when the force is applied at the center? [ 270 N ]
168. A 200 kg satellite is lifted to an orbit of 2.2×104 km radius. If radius and mass of the earth are 6400km and 6 x 1024 kg respectively, how much additional PE is required to lift the satellite? [ 8.87 x 109 J ]
169. The density of ice is 971 kg/m3 and the density of sea water is 1025 kg/m3. What fraction of iceberg is beneath the water surface? [ 0.947 : 1 ]
170. An iceberg having volume 2060 cc floats in sea water of density 1030 kg/m3 with a portion of 224 cc above the surface. Calculate the density of the ice. [ 0.89 g/cc ]
171. A bullet of mass 10g is fired from a gun of mass 1 kg with a velocity of 100 m/s. Calculate the ratio of the KE of the bullet and the gun. [ 100:1]
172. A coin placed on a disc rotates with speed of 331/3 rev/min provided that the coin is not more than 10 cm from the axis. Calculate the coefficient of static friction.
173. Speed of a body spinning about an axis increases from rest to 100 rev/min in 5 sec if a constant of 20 NM is applied. The torque is removed and the body comes to rest 100 sec due to friction. Calculate the frictional torque.
174. A 25 cm thick block of ice floating on fresh water can support a 80 kg man standing on it. What is the smallest area of the ice block? ( Sp gravity of ice = 0.917)
175. A small mass rests on a horizontal platform which vibrates in a SHM with a period of 0.25 s. Find the maximum amplitude of the motion which will allow the mass to remain in contact with platform thought the motion.
176. Calculate the period of the revolution of the satellite revolving at a distance of 20 km from the earth surface. ( R = 6400km, g = 10 m/s2 ) [ 5050.13 s ]
177. A train of mass 2 x 105 kg moves with speed 72 km / hr up a straight inclined plane against a frictional force 1.28 x 104 N. The inclination is such that it rises vertically 1.0 m for every 100 m traveled along the inclination. Calculate (i) the rate of increase per second of PE, (ii) the power developed by the train. [ 400, 656 kw]
178. A constant torque of 500 Nm turns a wheel of moment of inertia 20 kgm2 about its center. Find the angular velocity and KE gained in 2 second and KE gained. [ 50 rad/s, 25000J]
179. A simple pendulum 4m long swings with amplitude of 0.2m. Determine (i) velocity at its lowest point, (ii) acceleration at the end of the path.
[ 0.32 m/s,0.5m/s2]
180. A piece of gold aluminum alloy weighs 100g in air and 80g in water. What is the weight of the gold in the alloy if the relative density of gold is 19.3 and that of aluminum is 2.5
181. An object of mass 8 kg is whirled round in a vertical circle of radius 2m with a speed 6m/s. Calculate the maximum and minimum tension in the string.
[ 224N, 64N]
182. A body is projected horizontally from the top of a tower of height 100m with a velocity 9.8 m/s. Find the velocity with which it hits the ground. [ 45.8 m/s ]
183. A particle of mass 0.3 kg vibrates with a velocity 2sec. If its amplitude is 0.5m, what is its maximum KE? [ 0.37 J ]
184. A string supports a solid Iron of mass 200g totally immersed in liquid of density 800kg/m3. If the density of the iron is 8000 kg/m3, calculate the tension in the string. [ 1.8 N ]
185. An object is dropped from the top of a tower of height 156.8 m and at the same time, another object is thrown vertically upward with velocity 78.4 m/s from the foot of the tower. When and where will they meet? [ 2s, 20m from top]
186. A constant torque of 200 Nm turns a wheel which has a moment of inertia 100 kg m2 about its center. Find KE gained after 20 revolutions. [
187. The displacement y of a mass vibrating with SHM is given by y = 20 sin 10t. Where y is in millimeter and t is in second. What is (a) amplitude (b) period (c) velocity when t = 0. [ 0.002m, 0.2 s, 0.682 m/s]
188. An alloy of mass 588 gm and volume 100 cc is made of iron of density 8.0 g/cc and aluminum of density 2.7 g/cc. Calculate the proportion by (i) volume, (ii) by mass of the constituents of the alloy.
[(i) 6×10-5 m3, 4×10-5 m3 (ii) 0.48kg, 0.108 kg]
178. A constant torque of 500 Nm turns a wheel of moment of inertia 20 kgm2 about its center. Find the angular velocity and KE gained in 2 second and KE gained. [ 50 rad/s, 25000J]
179. A simple pendulum 4m long swings with amplitude of 0.2m. Determine (i) velocity at its lowest point, (ii) acceleration at the end of the path.
[ 0.32 m/s,0.5m/s2]
180. A piece of gold aluminum alloy weighs 100g in air and 80g in water. What is the weight of the gold in the alloy if the relative density of gold is 19.3 and that of aluminum is 2.5
181. An object of mass 8 kg is whirled round in a vertical circle of radius 2m with a speed 6m/s. Calculate the maximum and minimum tension in the string.
[ 224N, 64N]
182. A body is projected horizontally from the top of a tower of height 100m with a velocity 9.8 m/s. Find the velocity with which it hits the ground. [ 45.8 m/s ]
183. A particle of mass 0.3 kg vibrates with a velocity 2sec. If its amplitude is 0.5m, what is its maximum KE? [ 0.37 J ]
184. A string supports a solid Iron of mass 200g totally immersed in liquid of density 800kg/m3. If the density of the iron is 8000 kg/m3, calculate the tension in the string. [ 1.8 N ]
185. An object is dropped from the top of a tower of height 156.8 m and at the same time, another object is thrown vertically upward with velocity 78.4 m/s from the foot of the tower. When and where will they meet? [ 2s, 20m from top]
186. A constant torque of 200 Nm turns a wheel which has a moment of inertia 100 kg m2 about its center. Find KE gained after 20 revolutions. [
187. The displacement y of a mass vibrating with SHM is given by y = 20 sin 10t. Where y is in millimeter and t is in second. What is (a) amplitude (b) period (c) velocity when t = 0. [ 0.002m, 0.2 s, 0.682 m/s]
188. An alloy of mass 588 gm and volume 100 cc is made of iron of density 8.0 g/cc and aluminum of density 2.7 g/cc. Calculate the proportion by (i) volume, (ii) by mass of the constituents of the alloy.
[(i) 6×10-5 m3, 4×10-5 m3 (ii) 0.48kg, 0.108 kg]
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