$A$ ball of mass $0.1\, kg$ is whirled in a horizontal circle of radius $1\, m$ by means of a string at an initial speed of $10\, rpm$. Keeping the radius constant,the tension in the string is reduced to one-quarter of its initial value. The new speed is ....... $rpm$.

What is the value of the contact force $R$ on an object of mass $m$ placed on an inclined plane with angle $\theta$?

$A$ block of mass $5\,kg$ starting from rest is pulled up on a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal with an effective acceleration of $1\,m/s^2$. The power delivered by the pulling force at $t = 10\,s$ from the start is $.....\,W$. [Use $g = 10\,m/s^2$] (calculate the nearest integer value).

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth,while the lower half is rough. $A$ block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by:

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction,as shown in the figure. If the trolley is accelerated horizontally along the positive $x$-axis with $a_0$,then identify the correct statement$(s)$ related to the tension $T$ in the string.

An object of mass $M$ is placed on a rough horizontal surface (coefficient of friction $\mu$). $A$ person tries to pull the object by applying a horizontal force,but the object does not move. The force $F$ exerted by the surface on the object is: