Rate measure practice · Easy

If the volume of a spherical ball is increasing at the rate of $4 \pi \mathrm{cc} / \mathrm{sec}$, then the rate of increase of its radius (in cm/sec), when the volume is $288 \pi \mathrm{cc}$,

If the rate of increase of a side of a triangle inscribed in a circle of radius $\mathrm{R}$, is $\mathrm{R}$ times the rate of increase of the measure of opposite angle, then the measure of the angle is ....... .

The rate of change of the surface area of a sphere of a sphere of radiusr,when the radius is increasing at the rate of 2 cm/sis proportional to

A stone thrown upwards, has equation of motion $s = 490t - 49{t^2}.$ .Then, the maximum height reached by it ,is

If there is an error of $2\%$ in measuring the length of a simple pendulum, then percentage error in its period is

A rocket, weighing 9000 N fixed vertically upward. The gasses are expelled at a rate of $30\,\,{\text{kg}}\,{{\text{s}}^{ - 1}}$ with a speed of 0.6 km/s if the rocket weight 5000 N at the burnout, then the net upward force on the rocket at fire off should be

The displacement of a body along the X –axis depends on time as $\sqrt x = t + 2$ then the velocity of body

If a particle moves according to the law $s = 6{t^2} - \frac{{{t^3}}}{2}$, then the time at which it is momentarily at rest is

If a particle is moving with velocity $v\left( t \right) = \cos \,\,\pi t$ along a straight line such that at $t = 0,\;\,s = 4$ its position function is given by

A point is moving on $y = 4 - 2{x^2}$. The $x$-coordinate of the point is decreasing at the rate of 5 unit per second. Then, the rate at which $y$-coordinate of the point is changing when the point is at (1,2)is

The distance travelled by a motor car in $t$ seconds after the brakes are applied is s feet, where $s=22 t-12 t^2$. The distance travelled by the car before it stops, is

If $T=2 \pi \sqrt{\frac{l}{g}}$, then relative errors in $T$ and $l$ are in the ratio