Embibe Experts Solutions for Chapter: Centre of Mass, Momentum and Collisions, Exercise 3: Exercise - 3

Two balls having linear momenta ${\overrightarrow{p}}_1=p\hat{\mathrm{i}}$ and ${\overrightarrow{p}}_2=-p\hat{\mathrm{i}}$, undergo a collision in free space. There is no external force acting on the balls. Let ${\overrightarrow{p}}_1^{\text{'}}$ and ${\overrightarrow{p}}_2^{\text{'}}$ be their final momenta. The following option (s) is (are) not allowed for any non-zero value of $p, a_1, a_2, b_1, b_2, c_1$ and $c_2$.

A point mass of $1 \mathrm{kg}$ collides elastically with a stationary 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 statement(s) is (are) correct for the system of these two masses

A particle of mass $m$ is projected from the ground with the initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of the trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed $u_0$. The angle that the composite system makes with horizontal immediately after the collision is

A circular disc of radius $\mathrm{R}$  is removed from a bigger circular disc of radius $2\mathrm{R}$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\mathrm{\alpha R}$  from the centre of the bigger disc. The value of α 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:

Distance of the centre of mass of a solid uniform cone from its vertex is $z_0$. If the radius of its base is $R$ and its height is $h$ then $z_0$ is equal to

In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles after collision is

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that