Work, Energy & Power PYQs Set 9 (PDF)

Set 9 of 10 · Questions 241-270 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Work, Energy & Power · Set 9 (Q241-270)
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241. $A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :$ (1) $1 : 2$ (2) $3 : 2$ (3) $2 : 1$ (4) $1 : 1$ 242. $A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m . Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N . The total distance through which the box has been moved is 30 m . What is the work done by the person during the total movement of the box?$ (1) $5690 J$ (2) $3280 J$ (3) $5250 J$ (4) $2780 J$ 243. $A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point B is: ( Take g = 10 m / s^{2}).$ (1) $20 m / s$ (2) $10 m / s$ (3) $210 m / s$ (4) $10 m / s$ 244. $A bullet of mass 10 g moving horizontally with a velocity of 400 m s^{- 1} strikes a wood block of mass 2 kg which is suspended by light inextensible string of length 5 m . As a result, the centre of gravity of the block found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be (NEET‐II2016)$ (1) $100 m s^{- 1}$ (2) $80 m s^{- 1}$ (3) $120 m s^{- 1}$ (4) $160 m s^{- 1}$ 245. $A force F acting on an object varies with distance x as shown here. The force is in N and x in m . The work done by the force in moving the object from x = 0 to x = 6 m is X in (m)$ (1) $18.0 J$ (2) $13.5 J$ (3) $9.0 J$ (4) $4.5 J.$ 246. $A spring mass system (mass m, spring constant k and natural length l) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity ω, (k >> m ω^{2}) the relative change in the length of the spring is best given by the option:$ (1) $\frac{2}{3} (\frac{m ω ^{2}}{k})$ (2) $\frac{m ω ^{2}}{3 k}$ (3) $\frac{2 m ω ^{2}}{k}$ (4) $\frac{m ω ^{2}}{k}$ 247. $A truck accelerates from speed v to 2 v . Work done in acceleration the truck during this is$ (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) $less than the work done in accelerating it from rest to v .$ 248. $A ball of mass 10 g is allowed to fall down from 10 m height. After collision with the ground if 50 % of its energy is lost; then the height reached by the ball is$ (1) $4 m$ (2) $6 m$ (3) $5 m$ (4) $7 m$ 249. $A ball is thrown vertically downwards from a height of 20 m with an initial velocity v_{0} . It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v_{0} is (Take g = 10 m s^{- 2})$ (1) $28 m s^{- 1}$ (2) $10 m s^{- 1}$ (3) $14 m s^{- 1}$ (4) $20 m s^{- 1}$ 250. $A block moving horizontally on a smooth surface with a speed of 40m/s splits into two parts with masses in the ratio of 1:2. If the smaller part moves 60m/s at in the same direction, then the fractional change in kinetic energy is:-$ (1) $\frac{1}{3}$ (2) $\frac{2}{3}$ (3) $\frac{1}{8}$ (4) $\frac{1}{4}$ 251. $An object of mass 500 g, initially at rest acted upon by a variable force whose X component varies with X in the manner shown. The velocities of the object a point X = 8 m and X = 12 m, would be the respective values of (nearly) [NEET 2019]$ (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) $18 m / s and 20.6 m / s$ 252. $A bob of mass ' m' is suspended by a light string of length ' L'. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies \frac{( K . E . ) _{A}}{( K . E . ) _{B}} is:$ (1) $3 : 2$ (2) $5 : 1$ (3) $2 : 5$ (4) $1 : 5$ 253. $A uniform cable of mass ’ M ’ and length ’ L ’ is placed on a horizontal surface such that its (\frac{1}{n})^{th} part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:$ (1) $\frac{MgL}{2 n ^{2}}$ (2) $\frac{MgL}{n ^{2}}$ (3) $\frac{2 MgL}{n ^{2}}$ (4) $nMgL$ 254. $A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within Is, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is$ (1) $45m$ (2) $90m$ (3) $125m$ (4) $25m$ 255. $A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d . The net work done in the process is$ (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) $mg (h + d) + \frac{1}{2} k d^{2} .$ 256. $Two rectangular blocks A and B of masses 2 kg and 3 kg respectively are connected by a spring of spring constant 10.8 N m^{- 1} and are placed on a frictionless horizontal surface. The block A was given an initial velocity of 0.15 m s^{- 1} in the direction shown in the figure. The maximum compression of the spring during the motion is$ (1) $0.01 m$ (2) $0.02 m$ (3) $0.05 m$ (4) $0.03 m$ 257. $A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are, respectively [NEET 2021]$ (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) $\frac{S}{4}, \frac{3 gS}{2}$ 258. $An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 m / s . The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is (g = 10 m / s^{- 1}) [NEET 2022]$ (1) $23000$ (2) $20000$ (3) $34500$ (4) $23500$ 259. $A particle of mass M, starting from rest, undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is (Mains 2010)$ (1) $\frac{M V ^{2}}{T}$ (2) $\frac{M V ^{2}}{2 T ^{2}}$ (3) $\frac{M V ^{2}}{T ^{2}}$ (4) $\frac{M V ^{2}}{2 T}$ 260. $A person of mass M = 90 kg standing on a smooth horizontal plane of ice throws a body of mass m = 10 kg horizontally on the same surface. If the distance between the person and body after 10 s is 10 m, then the KE of the person (in J is)$ (1) $0.55 J$ (2) $4.5 J$ (3) $0.90 J$ (4) $o$ 261. $Given below are two statements : Statement I: An object moves from position r_{1} to position r_{2} under a conservative force field F . The work done by the force is W = - \sum F \cdot dr . Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. In the light of the above statements, choose the correct answer from the options given below :$ (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) $Both Statement I and Statement II are true$ 262. $A block of mass 25 kg is pulled along a rough horizontal surface by a force at an angle 4 5^{\circ} with the horizontal. The friction coefficient between the block and the surface is 0.25. The block travels at a uniform velocity. The work done by the applied force during a displacement of 5 m of the block is:$ (1) $490 J$ (2) $970 J$ (3) $735 J$ (4) $245 J$ 263. $A uniformly thick wheel with moment of inertial I and radius R is free to rotate about its centre of mass (see figure). A mass-less string is wrapped over its rim and two blocks of masses m_{1} and m_{2} (m_{1} > m_{2}) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when m_{1} descents by a distance h is:$ (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) $(\frac{m _{1} + m _{2}}{( m _{1} + m _{2} ) R ^{2} + I})^{\frac{1}{2}} g$ 264. $A square shaped hole of side I = \frac{a}{2} is carved out at a distance d = \frac{a}{2} from the center ’ O^{’} of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is - \frac{a}{x} value of X (to the nearest integer) is$ 265. $A force F = (2 + 3 x) i acts on a particle in the x direction where F is in Newton and x is in meter. The work done by this force during a displacement from x = 0 to x = 4 m is_____J.$ 266. $An engine is attached to a wagon through a shock absorber of length 1.5m. The system with a total mass of 40,000 is moving with a speed of 72 k m h^{- 1} when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0m. If 90%of energy of the wagon is lost due to friction, the spring constant is ....... x 1 0^{5} N/m$ 267. $The momentum of a body is increased by 50%. The percentage increase in the kinetic energy of the body is_________%.$ 268. $A particle of mass m is moving along the x -axis with initial velocity ı ˋ . It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If sin θ_{1} = n sin θ_{2} then value of n is$ 269. $Consider an elliptically shaped rail PQ in the vertical plane with OP = 3m and OQ= 4m. A block of mass 1kg is pulled along the rail from P to Q with a force of 18 N, Which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is (n \times 10) joules. The value of n is (take acceleration due to gravity = 10 m s^{-2})$ 270. $A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m . The maximum angular speed (in rad s^{- 1}) with which it can be rotated about its other end in space station is (Breaking stress of wire e = 4.8 \times 10^{7} N m^{- 2} and area of cross section of the wire = 10^{- 2} cm^{2} is$