Question

A mass of $3.9kg$ suspended from a string of length $0.5m$ is at rest. Another body of mass $0.1kg$ moving horizontally with a velocity $200m{s}^{-1}$ strikes and sticks to it. The maximum angle through which the system swings just before the tension in the string becomes zero is :

• A. ${60}^o$
• B. ${90}^o$
• C. ${120}^o$
• D. ${180}^o$

Answer 1

The correct option is D ${180}^o$

When a body of mass 0.1 kg moving with

velocity 200 m/s strikes a body of mass 3.9 kg

suspended by a string of length 0.5 m, after striking

both the bodies stick together,

So applying law of conservation of momentum,

$0.1\times 200=(3.9+0.1)v$

$v=5m/s$

After striking both the masses together move in a

vertical circle which satisfy the following equation of

motion for tension,

$T=\frac{m{v}^2}{l}+mgcos\theta$

But tension is zero at the highest point

the highest point velocity $v=\sqrt{gl}$

$0=mg+mgcos\theta$

$cos\theta =-1$

$\theta =\pi$