Non-uniform Circular Motion

The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.

Non-uniform motion involves a change in speed, which produces tangential acceleration. 

Find the angular acceleration if the angular velocity of a body in rotational motion changes from $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2 $}\right.\mathrm{rad}/\mathrm{s} \raisebox{1ex}{$\mathrm{to} 3\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4 $}\right.$in $0.4 \mathrm{s}.$

Is the tangential acceleration and speed are related? If YES, explain.

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

Body M and N are hung on two spring balance. The reading of the spring balances are as in the figure

Which of following statements are absolutely correct?

$1$. M's weight is smaller than N.

$2.$ M and N cannot be weighed together with the same spring balance

$3.$ The density of M is smaller than that of N

in figure I and II, forces parallel to the plane act on bodies X and Y, which are of frictionless horizontal plane.

 Accordingly, what can be said about the resultant ${\mathrm{R}}_{\mathrm{x}}, {\mathrm{R}}_{\mathrm{y}}$forces  acting on the objects?

$\mathrm{The} \mathrm{fraction} \mathrm{of} \mathrm{floating} \mathrm{body} \mathrm{of} \mathrm{volume} {\mathrm{V}}_0 \mathrm{and} \mathrm{density} {\mathrm{d}}_0 \mathrm{above} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{liquid} \mathrm{of} \mathrm{density} \mathrm{d} \mathrm{will} \mathrm{be}$?

A block of mass $5\mathrm{kg}$, exhibits circular motion with the mass decreasing at the rate of $0.5\raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{$\sec $}\right.$. At what time the centripetal forces will be zero on the block?

A ball tied at the end of a perfect string tied tightly $\left(\mathrm{as} \mathrm{fixed}\right)$ to a wooden bar at the other end is rotating with constant angular velocity. Its tangential velocity will ______.

If the thermal capacity of a body is, infinity then

If $10$g of ice at $0°$C mixes with $10$g of water at $10°$C, then the final temperature t is given by

A graph is plotted taking $°$C along the Y-axis and $°$F along the X-axis. It is a/an

A thermometer is used to measure 

Choose the correct statement:

The Coefficient of linear expansion always                      with the increase in temperature.

The block of wood is floating on water at $0°$C, with a certain volume V above water level. The temperature of the water is slowly raised from $0°$. How will volume V change with the rise in temperature?

Water evaporates under atmospheric pressure. without changing the temperature, the same water is placed in a partial vacuum. The rate of evaporation will

Two spheres of the same size are made of the same metal, but one is hollow and the other is solid. They are heated to the same temperature. Then,

The tangential velocity of a body in a non-uniform circular motion varies as $v=7t^2–2v$ with the radius being equal to $21 \mathrm{m}$. What is the angular acceleration at $\mathrm{t}=2 \mathrm{s}$ in $\mathrm{rad}/{\mathrm{s}}^2$?