When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ}$ with horizontal. it can travel a distance $\mathrm{x}_{1}$ along the plane. But when the inclination is decreased to $30^{\circ}$ and the same object the shot with the same velocity, it can travel $x_{2}$ distance. Then $x_{1}: x_{2}$ will be
$1: \sqrt{2}$
$\sqrt{2}: 1$
$1: \sqrt{3}$
$1: 2 \sqrt{3}$
A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will
A particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of plane of circle above vertex is $h$. The speed of particle should be
A particle moves with constant angular velocity in a circle. During the motion its
A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular speed of particle when the tension in the string at the top is zero ......... $rad/sec$
The ratio of angular speeds of minute hand and hour hand of a watch is