Question

A system of two blocks A and B are connected by an inextensible massless string as shown in figure. The pulley is massless and frictionless. Initially, the system is at rest. A bullet of mass 'm' moving with a velocity 'u' as shown hits block 'B' and gets embedded into it. The impulse imparted by tension force to the block of mass 3m is :

• A. $\frac{5mu}{4}$
• B. $\frac{4mu}{5}$
• C. $\frac{2mu}{5}$
• D. $\frac{3mu}{5}$

Answer 1

The correct option is D $\frac{3mu}{5}$

Let velocity of B and A after collision has magnitude $v$.

At the time of collision tension $=T$

Impulse provided by tension $=\int Tdt$

Consider change of momentum of (B + bullet)

$mu-\int Tdt=2mv$ ……… (i)

Consider change of momentum A

$\int Tdt=3mv$ …………..(ii)

From (i) and (ii),

$⟹mu=5mv$

$⟹v=\frac{u}{5}$

Hence, Impulse: $\int Tdt=3mv$

$⟹3m\left(\frac{u}{5}\right)=\frac{3mu}{5}$
Hence the correct option is $\left(D\right)$