Work, Energy & Power PYQs Set 8 (PDF)

Set 8 of 9 · Questions 211-240 of 248

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Mere Teacher · Previous Year Questions NEET Physics · Work, Energy & Power · Set 8 (Q211-240)
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211. $A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m / s . The ratio of its kinetic energies at point B and C is : (Take acceleration due to gravity as 10 m / s^{2})$ (1) $\frac{2 + 2}{3}$ (2) $\frac{2 + 3}{3}$ (3) $\frac{3 + 3}{2}$ (4) $\frac{3 - 2}{2}$ 212. $A mass of 0.5 kg moving with a speed of 1.5 m / s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N / m . The maximum compression of the spring would be$ (1) $0.15 m$ (2) $0.12 m$ (3) $1.5 m$ (4) $0.5 m$ 213. $A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :$ (1) $1 : 2$ (2) $3 : 2$ (3) $2 : 1$ (4) $1 : 1$ 214. $A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m . Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N . The total distance through which the box has been moved is 30 m . What is the work done by the person during the total movement of the box?$ (1) $5690 J$ (2) $3280 J$ (3) $5250 J$ (4) $2780 J$ 215. $A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point B is: ( Take g = 10 m / s^{2}).$ (1) $20 m / s$ (2) $10 m / s$ (3) $210 m / s$ (4) $10 m / s$ 216. $A bullet of mass 10 g moving horizontally with a velocity of 400 m s^{- 1} strikes a wood block of mass 2 kg which is suspended by light inextensible string of length 5 m . As a result, the centre of gravity of the block found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be (NEET‐II2016)$ (1) $100 m s^{- 1}$ (2) $80 m s^{- 1}$ (3) $120 m s^{- 1}$ (4) $160 m s^{- 1}$ 217. $A force F acting on an object varies with distance x as shown here. The force is in N and x in m . The work done by the force in moving the object from x = 0 to x = 6 m is X in (m)$ (1) $18.0 J$ (2) $13.5 J$ (3) $9.0 J$ (4) $4.5 J.$ 218. $A spring mass system (mass m, spring constant k and natural length l) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity ω, (k >> m ω^{2}) the relative change in the length of the spring is best given by the option:$ (1) $\frac{2}{3} (\frac{m ω ^{2}}{k})$ (2) $\frac{m ω ^{2}}{3 k}$ (3) $\frac{2 m ω ^{2}}{k}$ (4) $\frac{m ω ^{2}}{k}$ 219. $A truck accelerates from speed v to 2 v . Work done in acceleration the truck during this is$ (1) $three times as the work done in accelerating it from rest to v$ (2) $same as the work done in accelerating it from rest to v$ (3) $four times as the work done in accelerating it from rest to v$ (4) $less than the work done in accelerating it from rest to v .$ 220. $A ball of mass 10 g is allowed to fall down from 10 m height. After collision with the ground if 50 % of its energy is lost; then the height reached by the ball is$ (1) $4 m$ (2) $6 m$ (3) $5 m$ (4) $7 m$ 221. $A ball is thrown vertically downwards from a height of 20 m with an initial velocity v_{0} . It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v_{0} is (Take g = 10 m s^{- 2})$ (1) $28 m s^{- 1}$ (2) $10 m s^{- 1}$ (3) $14 m s^{- 1}$ (4) $20 m s^{- 1}$ 222. $A block moving horizontally on a smooth surface with a speed of 40m/s splits into two parts with masses in the ratio of 1:2. If the smaller part moves 60m/s at in the same direction, then the fractional change in kinetic energy is:-$ (1) $\frac{1}{3}$ (2) $\frac{2}{3}$ (3) $\frac{1}{8}$ (4) $\frac{1}{4}$ 223. $An object of mass 500 g, initially at rest acted upon by a variable force whose X component varies with X in the manner shown. The velocities of the object a point X = 8 m and X = 12 m, would be the respective values of (nearly) [NEET 2019]$ (1) $18 m / s and 24.4 m / s$ (2) $23 m / s and 24.4 m / s$ (3) $23 m / s and 20.6 m / s$ (4) $18 m / s and 20.6 m / s$ 224. $A bob of mass ' m' is suspended by a light string of length ' L'. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies \frac{( K . E . ) _{A}}{( K . E . ) _{B}} is:$ (1) $3 : 2$ (2) $5 : 1$ (3) $2 : 5$ (4) $1 : 5$ 225. $A uniform cable of mass ’ M ’ and length ’ L ’ is placed on a horizontal surface such that its (\frac{1}{n})^{th} part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:$ (1) $\frac{MgL}{2 n ^{2}}$ (2) $\frac{MgL}{n ^{2}}$ (3) $\frac{2 MgL}{n ^{2}}$ (4) $nMgL$ 226. $A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within Is, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is$ (1) $45m$ (2) $90m$ (3) $125m$ (4) $25m$ 227. $A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d . The net work done in the process is$ (1) $mg (h + d) - \frac{1}{2} k d^{2}$ (2) $mg (h - d) - \frac{1}{2} k d^{2}$ (3) $mg (h - d) + \frac{1}{2} k d^{2}$ (4) $mg (h + d) + \frac{1}{2} k d^{2} .$ 228. $Two rectangular blocks A and B of masses 2 kg and 3 kg respectively are connected by a spring of spring constant 10.8 N m^{- 1} and are placed on a frictionless horizontal surface. The block A was given an initial velocity of 0.15 m s^{- 1} in the direction shown in the figure. The maximum compression of the spring during the motion is$ (1) $0.01 m$ (2) $0.02 m$ (3) $0.05 m$ (4) $0.03 m$ 229. $A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are, respectively [NEET 2021]$ (1) $\frac{S}{4}, \frac{3 gS}{2}$ (2) $\frac{S}{4}, \frac{3 gS}{2}$ (3) $\frac{S}{2}, \frac{3 gS}{2}$ (4) $\frac{S}{4}, \frac{3 gS}{2}$ 230. $An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 m / s . The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is (g = 10 m / s^{- 1}) [NEET 2022]$ (1) $23000$ (2) $20000$ (3) $34500$ (4) $23500$ 231. $A particle of mass M, starting from rest, undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is (Mains 2010)$ (1) $\frac{M V ^{2}}{T}$ (2) $\frac{M V ^{2}}{2 T ^{2}}$ (3) $\frac{M V ^{2}}{T ^{2}}$ (4) $\frac{M V ^{2}}{2 T}$ 232. $A person of mass M = 90 kg standing on a smooth horizontal plane of ice throws a body of mass m = 10 kg horizontally on the same surface. If the distance between the person and body after 10 s is 10 m, then the KE of the person (in J is)$ (1) $0.55 J$ (2) $4.5 J$ (3) $0.90 J$ (4) $o$ 233. $Given below are two statements : Statement I: An object moves from position r_{1} to position r_{2} under a conservative force field F . The work done by the force is W = - \sum F \cdot dr . Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. In the light of the above statements, choose the correct answer from the options given below :$ (1) $Both Statement I and Statement II are false$ (2) $Statement I is false but Statement II is true$ (3) $Statement I is true but Statement II is false$ (4) $Both Statement I and Statement II are true$ 234. $A block of mass 25 kg is pulled along a rough horizontal surface by a force at an angle 4 5^{\circ} with the horizontal. The friction coefficient between the block and the surface is 0.25. The block travels at a uniform velocity. The work done by the applied force during a displacement of 5 m of the block is:$ (1) $490 J$ (2) $970 J$ (3) $735 J$ (4) $245 J$ 235. $A uniformly thick wheel with moment of inertial I and radius R is free to rotate about its centre of mass (see figure). A mass-less string is wrapped over its rim and two blocks of masses m_{1} and m_{2} (m_{1} > m_{2}) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when m_{1} descents by a distance h is:$ (1) $(\frac{m _{1} + m _{2}}{( m _{1} + m _{2} ) R ^{2} + I})^{\frac{1}{2}} g h$ (2) $(\frac{2 ( m _{1} - m _{2} ) g h}{( m _{1} + m _{2} ) R ^{2} + I})^{\frac{1}{2}}$ (3) $(\frac{2 ( m _{1} + m _{2} ) g h}{( m _{1} + m _{2} ) R ^{2} + I})^{\frac{1}{2}}$ (4) $(\frac{m _{1} + m _{2}}{( m _{1} + m _{2} ) R ^{2} + I})^{\frac{1}{2}} g$ 236. $A bead of mass ' m' slides without friction on the wall of a vertical circular hoop of radius ' R' as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is ' R'. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity)$ (1) $3 Rg + \frac{kR ^{2}}{m}$ (2) $2 gR + \frac{KR ^{2}}{m}$ (3) $2 Rg + \frac{KR ^{2}}{m}$ (4) $2 Rg + \frac{4 R ^{2}}{m}$ 237. $A spring has a natural length l with one end fixed to the ceiling. The other end is fitted with a smooth ring which can slide on a horizontal rod fixed at distance l below the ceiling.Initially, the spring makes an angle of 60^{\circ} with the vertical, when system is released from test. Find the angle of the spring with the vertical, when, the velocity of the ring reaches half of the maximum velocity, which the ring can attain during the motion.$ (1) $30^{\circ}$ (2) $cos^{- 1} (\frac{2}{2 + 3})$ (3) $cos^{- 1} (\frac{3 - 1}{2})$ (4) $Non e$ 238. $A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60^{\circ} with vertical as shown in figure. At distance of 1 m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by bob A, then radius R is____m.$ (1) $\frac{1}{5}$ (2) $\frac{2 - 3}{5}$ (3) $\frac{3}{5}$ (4) $\frac{2 + 3}{5}$ 239. $A bead P sliding on a frictionless semi-circular string (ACB) and it is at point S at t = 0 and at this instant the horizontal component of its velocity is v . Another bead Q of the same mass as P is ejected from point A at t = 0 along the horizontal string AB, with the speed v, friction between the beads and the respective strings may be neglected in both cases. Let t_{P} and t_{Q} be the respective times taken by beads P and Q to reach the point B, then the relation between t_{P} and t_{Q} is$ (1) $t_{P} < t_{Q}$ (2) $t_{P} > t_{Q}$ (3) $t_{P} = t_{Q}$ (4) $t_{P} > 1.25 t_{Q}$ 240. $In the case of non-conservative forces, the following statement is correct.$ (1) $The work done by non-conservative force in a closed path is zero.$ (2) $The work done by non-conservative forces does not depend on the path.$ (3) $The work done by non-conservative forces depend on the path.$ (4) $There is no energy loss in case of non-conservative forces.$