K K Sharma Solutions for Chapter: Centre of Mass, Momentum Conservation and Collision, Exercise 1: TOPICWISE QUESTIONS

Two objects of masses $200 \mathrm{gm}$ and $500 \mathrm{gm}$ possess velocities $10î$ and $\left(3\hat{\mathit{i}}+5\hat{j}\right) \mathrm{m} {\mathrm{s}}^{-1}$, respectively. The velocity of their centres of masses in $\mathrm{m} {\mathrm{s}}^{-1}$ is

The velocity of centre of mass of the system as shown in the figure is

Three particles of masses $1 \mathrm{kg}$, $2 \mathrm{kg}$ and $3 \mathrm{kg}$ are subjected to forces $\left(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}+2\hat{\mathrm{k}}\right) \mathrm{N}$, $\left(-\hat{\mathrm{i}} +2\hat{\mathrm{j}} -\hat{\mathrm{k}}\right) \mathrm{N}$ and $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\right) \mathrm{N}$, respectively. The magnitude of the acceleration of the COM of the system is

Two bodies of mass $10 \mathrm{kg}$ and $2 \mathrm{kg}$ are moving with velocity $\left(2\hat{\mathrm{i}}-7\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right) \mathrm{m} {\mathrm{s}}^{-1}$ and $\left(-10\hat{\mathrm{i}}+35\hat{\mathrm{j}}-3\hat{\mathrm{k}}\right) \mathrm{m} {\mathrm{s}}^{-1}$, respectively. The velocity of their centre of mass is

A block of mass $0.50 \mathrm{kg}$ is moving with a speed of $2.00 \mathrm{m} {\mathrm{s}}^{-1}$ on a smooth surface. It strikes another mass of $1.00 \mathrm{kg}$ and then, they move together as a single body. The energy loss during the collision is

Three balls $A\mathit{,}\mathit{ }B$ and $C$ $\left(m_{\mathrm{A}}=m_{\mathrm{C}}=4m_{\mathrm{B}}\right)$ are placed on a smooth horizontal surface. Ball $B$ collides with ball $C$ with an initial velocity $\text{ν}$, as shown in the figure. Total number of collisions between the balls will be (all collisions are elastic)

A particle moving horizontally collides with a fixed plane inclined at $60°$ to the horizontal. If it bounces vertically, the coefficient of restitution is

A point mass of $1 \mathrm{kg}$ collides elastically with a stationary point mass of $5 \mathrm{kg}$. After their collision, the $1 \mathrm{kg}$ mass reverses its direction and moves with a speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$. Which of the following statements is correct for a system of these two masses?