A particle is moving in a circle of radius $R$ with constant speed $v$, if radius is double then its centripetal force to keep the same speed should be
Doubled
Halved
Quadrupled
Unchanged
A person with his hands in his pockets is skating on ice at the velocity of $10 \,m/s$ and describes a circle of radius $50\, m$. What is his inclination with vertical
A car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud, as it leaves the ground are thrown
For a vehicle moving on a banked curved road, using free body diagram $(FBD)$, obtain the formula for the maximum safe speed $(v_{max})$.
A car turns a corner on a slippery road at a constant speed of $10\,m/s$. If the coefficient of friction is $0.5$, the minimum radius of the arc in meter in which the car turns is
At time $t=0$, a disk of radius $1 m$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}{3} rad s ^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{\pi} s$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $m$ ) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. The value of $x$ is. . . . . . .[Take $g=10 m s ^{-2}$.]