BM Sharma Solutions for Chapter: Motion in Two Dimensions, Exercise 6: DPP

What is the value of linear velocity, if $\overrightarrow{\omega }=3\hat{\mathrm{i}}-4\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{r}=5\hat{\mathrm{i}}-6\hat{\mathrm{j}}+6\hat{\mathrm{k}}$?

When a ceiling fan is switched off, its angular velocity reduces to $50 \mathrm{\%}$ while it makes $36$ rotations. How many more rotation will it make before coming to rest (assume uniform angular retardation)?

A car is moving with speed $30\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ on a circular path of radius $500\mathrm{ }\mathrm{m}$. Its speed is increasing at the rate of $2\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$, what is the acceleration of the car?

A car is travelling with linear velocity $v$ on a circular road of the radius $r$. If it is increasing its speed at the rate of $a \mathrm{m} {\mathrm{s}}^{-2}$, then the resultant acceleration will be

A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $\overrightarrow{a}$ is correctly shown in

A stone is projected from level ground at $t=0 \mathrm{s}$ such that, its horizontal and vertical components of initial velocity are $10 \mathrm{m} {\mathrm{s}}^{-1}$ and $20\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$, respectively. Then, the instant of time, at which the tangential and normal component of acceleration of the stone is same, is (neglect air resistance and $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$)

A particle is acted upon by a force of constant magnitude, which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that

For a particle performing uniform circular motion, choose the correct statement(s) from the following.