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Work, Energy and Power · Question 24

JEE Main 2025 (Online) 29th January Morning ShiftMCQMedium📈 Topic in 10% papers+4−1
1

As shown below, bob A of a pendulum having massless string of length 'R' is released from 60 to the vertical. It hits another bob B of half the mass that is at rest on a frictionless table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.) [figure]

  1. 43 Rg
  2. 13 Rg
  3. Rg
  4. 23 Rg

Answer

(2) 13 Rg

Solution

Fall in height of A: h = R - R 60 = R2

Speed of A just before collision: u = 2gh = gR

Elastic collision of m1 = m with m2 = m2 at rest:

v1 = m1 - m2m1 + m2u = m - m2m + m2u

v1 = 13u = 13 Rg

Answer: (2)

JEE Main 2025 (Online) 29th January Morning Shift

Keep practising — Work, Energy and Power

2

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 acceleration due to gravity) [figure]

  1. 2Rg + kR2m
  2. 3Rg + kR2m
  3. 2Rg + 4kR2m
  4. 2 gR + kR2m
JEE Main 2025 (Online) 28th January Morning Shift
3

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R In the light of the above statements, choose the most appropriate answer from the options given below

  1. A is false but R is true
  2. Both A and R are true but R is NOT the correct explanation of A
  3. A is true but R is false
  4. Both A and R are true and R is the correct explanation of A
JEE Main 2025 (Online) 28th January Morning Shift
4

A body of mass 4 kg is placed on a plane at a point P having coordinates (3, 4) m. Under the action of force F = (2 i + 3 j) N, it moves to a new point Q having coordinates (6, 10) m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of :

  1. 4 : 3
  2. 13 : 6
  3. 1 : 2
  4. 6 : 13
JEE Main 2025 (Online) 28th January Evening Shift

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