Question

A simple pendulum of length 1 m has wooden bob or mass 1 kg. It is struck by a bullet of mass $2 \times 10 ^ { 2 } \mathrm {~ms} ^ { - 1 }$. The height to which the bob rises before swinging back is (Take $\mathrm { g } = 10 \mathrm {~ms} ^ { - 2 }$)

• A. 0.2 m
• B. 0.6 m
• C. 8 m
• D. 1 m

Answer 1

Answer: (A)

0.2 m

Answer 2

Momentum of bullet

Let the combined velocity of the bob + bullet = v.

$= \left( 10 ^ { - 2 } + 1 \right) \mathrm { v } = 1.01 \mathrm { v }$

By conservation of momentum,

$1.01 \mathrm { v } = 2 \mathrm {~kg} \mathrm {~ms} ^ { - 1 }$

Or $\mathrm { v } = \frac { 2 } { 1.01 } = 1.98 \mathrm {~ms} ^ { - 1 }$

By conservation of energy

$\frac { 1 } { 2 } ( m + m ) v ^ { 2 } ( M + m ) g h$

Or s