# GATE Questions & Answers of Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

## What is the Weightage of Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions in GATE Exam?

Total 11 Questions have been asked from Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions topic of Engineering Mechanics subject in previous GATE papers. Average marks 1.55.

A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, $t=0$. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 $m/s^2$ and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of

A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area = 100 mm2, length = 1 m, Young's moduls = 100 GPa) from a height H of 10 mm as shown (Figure is not to scale). If g = 10 m/s2, the maximum compression of the elastic bar is ____________mm.

A point mass having mass $M$ is moving with a velocity $V$ at an angle $\theta$ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is

A mass of 2000 kg is currently being lowered at a velocity of 2 m/s from the drum as shown in the figure. The mass moment of inertia of the drum is $150\mathrm{kg}-\mathrm m^2$. On applying the brake, the mass is brought to rest in a distance of 0.5 m. The energy absorbed by the brake (in kJ) is __________

A system of particles in motion has mass center $G$ as shown in the figure. The particle $i$ has mass $m_i$ and its position with respect to a fixed point $O$ is given by the position vector ${\boldsymbol r}_\mathbf i$. The position of the particle with respect to $G$ is given by the vector ${\boldsymbol\rho}_\mathbf i$. The time rate of change of the angular momentum of the system of particles about $G$ is

(The quantity ${\overset{\boldsymbol.\boldsymbol.}{\mathbf\rho}}_\mathbf i\boldsymbol\infty$ indicates second derivative of ${\boldsymbol p}_\mathbf i$ with respect to time and likewise for $\boldsymbol r\boldsymbol i$ ).

A ball of mass 0.1 kg, initially at rest, is dropped from height of 1 m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20% . The height (in m) to which the ball will rise is _____.

A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be____.

A mass m1 of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m2 of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is

The coefficient of restitution of a perfectly plastic impact is