A car is moving with a constant speed of $20\,m / s$ in a circular horizontal track of radius $40\,m$. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take $g =10$ $\left.m / s ^2\right)$
$\frac{\pi}{6}$
$\frac{\pi}{2}$
$\frac{\pi}{4}$
$\frac{\pi}{3}$
In a conical pendulum, the bob is rotated with different angular velocities and tension in the string is calculated for different values of $\omega$ . Which of them is correct graph between $T$ & $\omega .$
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 $g=10 m s ^{-2}$.]
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
A $70 \;kg$ man stands in contact against the inner wall of a hollow cylindrical drum of radius $3\; m$ rotating about its vertical axis with $200\; rev/min$. The coefficient of friction between the wall and his clothing is $0.15 .$ What is the minimum rotational speed (in $rad/s$) of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?
A car moves along a circular track of radius $R$ banked at an angle of $30^o$ to the horizontal. The coefficient of static friction between the wheels and the track is $\mu$ . The maximum speed with which the car can move without skidding out is