Question

Two masses $2m$ and $m$ are connected by an inextensible light string. The string is passing over a light frictionless pulley. The mass $2m$ is resting on a surface and mass $m$ is hanging in air as shown in Fig. A particle of mass $m$ strikes the mass $m$ from below in case (I) with a velocity $v_0$ and in case (II) strikes mass $m$ with a velocity $v_0$ from top and sticks to it in both cases. Then,

• A. The conservation of linear momentum can be applied in both the cases just before and just after collision
• B. The conservation of linear momentum can be applied in case I but cannot be applied in case II just before and just after collision
• C. The ratio of velocities of mass $m$ just after collision in first and second cases is $\frac{1}{2}$
• D. The ratio of velocities of mass $m$ just after collision in first and second case is 2.

Answer 1

Answer: (B), (D)

The ratio of velocities of mass $m$ just after collision in first and second case is 2.

In the first case: $(m+m)v_1=m{v}_0\Rightarrow v_1=\frac{v_0}{2}$
In the second case:
$-\int Tdt=(m+m)v-m{v}_0$ (i)
$\int Tdt=2mv$ (ii)
From Eqs. (i) and (ii),
$4mv=m{v}_0\Rightarrow v=\frac{v_0}{4}$ and required ratio = 2