A particle of mass $m$ is released from the top of a hemisphere of radius $R.$ When the particle reached at the bottom has speed $v.$ Find the normal reaction on the particle by the hemisphere.

A car moves on a straight road with uniform speed. Normal reaction at $A, B$ and $C$ are $N_A, N_B$ and $N_C$ respectively, then

A car is taking a turn of radius $400 \mathrm{m}$ on a horizontal circle. Coefficient of friction between the ground and tyres of car is $0.2.$ Find the maximum speed with a safe turn can be taken.

Find the angle of banking for safe turn of radius $20 \mathrm{m},$ with speed $10 \mathrm{m} {\mathrm{s}}^{-1}.$(Given: $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and neglect friction)

A ball of mass  $\text{'}m\text{'}$ is rotating in a circle of radius$\text{'}r\text{'}$ ' with speed $v$ inside a smooth cone as shown in figure. Let $N$ be the normal reaction on the ball by the cone, then choose the wrong option.

A particle of mass $m$ is whirled in horizontal circle with the help of two threads of length $l$ each as shown in figure. Angular velocity equals $\omega$, then

A uniform rod is held at rest against a rough wall and a rough floor. Which of the following represents correct free body diagram of rod? (All standard symbols used)