Work, Energy & Power PYQs Set 10 (PDF)

Set 10 of 10 · Questions 271-294 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Work, Energy & Power · Set 10 (Q271-294)
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271. $A bead of mass ' m' slides without friction on the wall of a vertical circular hoop of radius ' R' as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is ' R'. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity)$ (1) $3 Rg + \frac{kR ^{2}}{m}$ (2) $2 gR + \frac{KR ^{2}}{m}$ (3) $2 Rg + \frac{KR ^{2}}{m}$ (4) $2 Rg + \frac{4 R ^{2}}{m}$ 272. $A spring has a natural length l with one end fixed to the ceiling. The other end is fitted with a smooth ring which can slide on a horizontal rod fixed at distance l below the ceiling.Initially, the spring makes an angle of 60^{\circ} with the vertical, when system is released from test. Find the angle of the spring with the vertical, when, the velocity of the ring reaches half of the maximum velocity, which the ring can attain during the motion.$ (1) $30^{\circ}$ (2) $cos^{- 1} (\frac{2}{2 + 3})$ (3) $cos^{- 1} (\frac{3 - 1}{2})$ (4) $Non e$ 273. $A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60^{\circ} with vertical as shown in figure. At distance of 1 m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by bob A, then radius R is____m.$ (1) $\frac{1}{5}$ (2) $\frac{2 - 3}{5}$ (3) $\frac{3}{5}$ (4) $\frac{2 + 3}{5}$ 274. $A bead P sliding on a frictionless semi-circular string (ACB) and it is at point S at t = 0 and at this instant the horizontal component of its velocity is v . Another bead Q of the same mass as P is ejected from point A at t = 0 along the horizontal string AB, with the speed v, friction between the beads and the respective strings may be neglected in both cases. Let t_{P} and t_{Q} be the respective times taken by beads P and Q to reach the point B, then the relation between t_{P} and t_{Q} is$ (1) $t_{P} < t_{Q}$ (2) $t_{P} > t_{Q}$ (3) $t_{P} = t_{Q}$ (4) $t_{P} > 1.25 t_{Q}$ 275. $In the case of non-conservative forces, the following statement is correct.$ (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) $There is no energy loss in case of non-conservative forces.$ 276. $Sand is being dropped from a stationary dropper at a rate of 0.5 k g s^{- 1} on a conveyor belt moving with a velocity of 5 m s^{- 1} . The power needed to keep belt moving with the same velocity will be:$ (1) $1.25W$ (2) $2.5W$ (3) $6.25 W$ (4) $12.5 W$ 277. $A block (b) is attached to two unstretched springs S1 and S2 with spring constants k and 4 k, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio \frac{y}{x} Figure:$ (1) $4$ (2) $2$ (3) $\frac{1}{2}$ (4) $\frac{1}{4}$ 278. $A shell, in flight, explodes into four unequal parts. Which of the following is conserved?$ (1) $Potential energy$ (2) $Momentum$ (3) $Kinetic energy$ (4) $Both (a) and (c).$ 279. $What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop? (NEET‐I2016)$ (1) $3 gR$ (2) $5 gR$ (3) $gR$ (4) $2 gR$ 280. $An artillery piece of mass M_{1} fires a shell of mass M_{2} horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is :$ (1) $M_{1} / (M_{1} + M_{2})$ (2) $\frac{M _{2}}{M _{1}}$ (3) $M_{2} / (M_{1} + M_{2})$ (4) $\frac{M _{1}}{M _{2}}$ 281. $From a fixed support, two small identical spheres are suspended by means of strings of length 1 m each. They are pulled aside as shown and then released. B is the mean position. Then the two spheres collide,$ (1) $at B after 0.25 second$ (2) $at B after 0.5 second$ (3) $none of the above$ (4) $on the right side of B when the strings are inclined at 15^{\circ} with B.$ 282. $Identify the correct statements from the following: (A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. (B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. (C) Work done by friction on a body sliding down an inclined plane is positive, (D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity in zero. (E) Work done by the air resistance on an oscillating pendulum in negative. Choose the correct answer from the options given below:$ (1) $B and E only$ (2) $A and C only$ (3) $B, D and E only$ (4) $B and D only$ 283. $A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the center. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is x (u^{2} - g L) .The value of x is$ (1) $3$ (2) $2$ (3) $1$ (4) $5$ 284. $A small block starts slipping down from a point B on an inclined plane AB, which is making an angle θ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction μ . It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2 AC, the coefficient of friction is given by μ = ktan θ .The value of k is _________.$ 285. $A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in m s^{-1}) of the particle is zero, the speed (in m s^{-1}) after 5s is$ 286. $An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle θ (as shown in figure) between the direction of force and horizontal varies as θ = kx, where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be E = \frac{n}{k} s in θ . The value of n is ____.$ 287. $A 0.5 kg block moving at a speed of 12 m s^{- 1} compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be___________N m^{- 1} .$ 288. $A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60° with vertical as shown in the figure. After releasing the bob. the maximum velocity attained by the bob will be_____________ms_{-}^{1} . (if g=10m/ s^{2})$ 289. $A force of F =_{(} 5 y + 2 0_{)} j^N acts on a particle. The work done by this force when the particle is moved from y=0m to y=10m is J$ 290. $Two persons A and B perform same amount of work in moving a body through a certain distance with application of forces acting at angle 4 5^{0} and 6 0^{0} with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is \frac{1}{x} . The value of x is$ 291. $The center of mass of a solid hemisphere of radius 8 cm is xcm from the centre of the flat surface. Then value of x is$ 292. $A force F = (5 + 3 y^{2}) acts on a particle in the y-direction, where F is newton and y is in meter. The work done by the force during a displacement from y = 2m to y = 5m is______j.$ 293. $A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4s is \frac{1}{3} α^{2} P m . The value of α will be......$ 294. $A small particle moves to position 5 i^- 2 j^+ k^from its initial position 2 i^+ 3 j^- 4 k^under the action of force 5 i^+ 2 j^+ 7 k^N . The value of work done will be _________J.$