For circular motion, if ${\vec a_t},\,{\vec a_c},\,\vec r$ and $\vec v$ are tangential acceleration, centripetal acceleration, radius vector and velocitym respectively, then find the wrong relation
${\vec a_t}.{\vec a_c} = 0$
${\vec a_t}.\vec v$ may be positive or negative
${\vec a_c}.\vec v$ may be positive or negative
${\vec a_c}.\vec v = 0$
A small block slides down from rest at point $A$ on the surface of a smooth cylinder, as shown. At point $B$, the block falls off (leaves) the cylinder. The equation relating the angles $\theta_1$ and $\theta_2$ is given by
The second's hand of a watch has length $6\,\, cm$. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be
The ratio of period of oscillation of the conical pendulum to that of the simple pendulum is : (Assume the strings are of the same length in the two cases and $\theta$ is the angle made by the string with the verticla in case of conical pendulum)
If a particle moves in a circle describing equal angles in equal times, its velocity vector
A clock has $75 \mathrm{~cm}, 60 \mathrm{~cm}$ long second hand and minute hand respectively. In $30$ minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi=3.14$ ) :