A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed v/3 and the bob just completes the vertical circle. The value of v is ___________ ms______1. (if g = 10 m/s2). Numerical answer type. Work it out, then open the answer.

Answer: 10. To just complete the vertical circle the bob needs u = √(5gl) = √(5 × 10 × 2) = 10 m/s at the bottom. Momentum conservation: 0.075 v = 0.075 · v/3 + 0.05 × 10 0.05 v = 0.5 ⇒ v = 10 m/s So v = 10 m s ⁻¹.

A pendulum of length 2 m consists of a wooden bob of mass 50 g. A… | JEE Main 2022 (27 Jun, Shift 1)

Q11JEE Main 2022 · 27 JUN · SHIFT 1Difficult

Critical Speed & Looping

A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of v is ___________ ms______1. (if g = 10 m/s2).

Numerical answer type. Work it out, then open the answer.

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Answer: 10

To just complete the vertical circle the bob needs $u = \sqrt{5gl} = \sqrt{5 \times 10 \times 2} = 10$ m/s at the bottom.
Momentum conservation: $0.075\,v = 0.075 \cdot \frac{v}{3} + 0.05 \times 10$
$0.05\,v = 0.5 \Rightarrow v = 10$ m/s
So $v = 10$ m s $^{-1}$ .

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