A particle, moving with uniform speed $v$, changes its direction by angle $\theta$ in time $t$. Magnitude of its average acceleration during this time is
zero
$\frac{2 v}{t} \sin \frac{\theta}{2}$
$\frac{v \sqrt{2}}{t}$
None of these
The average acceleration vector for a particle having a uniform circular motion is
A particle is rotating in a circle of radius $1\,m$ with constant speed $4\,m / s$. In time $1\,s$, match the following (in $SI$ units) columns.
Colum $I$ | Colum $II$ |
$(A)$ Displacement | $(p)$ $8 \sin 2$ |
$(B)$ Distance | $(q)$ $4$ |
$(C)$ Average velocity | $(r)$ $2 \sin 2$ |
$(D)$ Average acceleration | $(s)$ $4 \sin 2$ |
An aircraft executes a horizontal loop of radius $1.00\; km$ with a steady speed of $900 \;km/h$. Compare its centripetal acceleration with the acceleration due to gravity.
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
A car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take same time to complete the circles, the ratio of their angular speeds and linear speeds will be .........