JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Conservation of Momentum

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A bullet of 10 g , moving with velocity v , collides head-on with the stationary bob of a pendulum and recoils with velocity

100 m / s

. The length of the pendulum is 0.5 m and mass of the bob is 1 kg . The minimum value of

v =

____

m / s

so that the pendulum describes a circle. (Assume the string to be inextensible and

g = 10 m / s^{2}

)

Answer: 400

Solution

To barely complete the vertical circle the bob needs a lowest-point speed

v_{bottom} = 5 g L = 5 \times 10 \times 0.5 = 5

m/s. Momentum is conserved in the head-on collision; taking the bullet's incoming direction as positive and noting it rebounds at

100

m/s,

(0.01) v = (1) (5) + (0.01) (- 100),

0.01 v = 5 - 1 = 4

and

v = 400

m/s. The minimum bullet speed is

400

m/s.

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Integer answer

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