A force $F = (6\hat{i} - 8\hat{j} + 10\hat{k})\text{ N}$ produces an acceleration of $1\text{ m/s}^2$ in a body. Calculate mass of the body.
2.
A cricket ball of mass $150\text{ g}$ moving at $20\text{ m/s}$ is caught by a player in $0.1\text{ s}$. Find impulse and average force exerted on player's hand.
Section B: Connected Bodies & Pulleys
3.
Two masses $m_1 = 3\text{ kg}$ and $m_2 = 5\text{ kg}$ are connected by a light string passing over a smooth pulley (Atwood machine). Find acceleration $a$ and string tension $T$.
4.
A block of mass $m=2\text{ kg}$ rests on an inclined plane of angle $\theta = 30^\circ$. Find normal reaction and force of friction required for equilibrium.
Section C: Friction & Banking of Roads
5.
A car of mass $1000\text{ kg}$ negotiates a banked curve of radius $R = 50\text{ m}$ at angle $\theta = 45^\circ$. Find optimum speed for zero friction.
6.
Define angle of friction $\lambda$ and angle of repose $\theta_{repose}$, and prove $\mu_s = \tan\lambda = \tan\theta_{repose}$.
