$A$ $10 \, kg$ ball attached to the end of a rigid massless rod of length $L = 1 \, m$ rotates at a constant speed in a horizontal circle of radius $r = 0.5 \, m$ and period $T = 1.57 \, s$ as shown in the figure. The force exerted by the rod on the ball is ........ $N$.

$A$ small block of mass $0.1 \ kg$ lies on a fixed inclined plane $PQ$ which makes an angle $\theta$ with the horizontal. $A$ horizontal force of $1 \ N$ acts on the block through its center of mass as shown in the figure. The block remains stationary if (take $g = 10 \ m/s^2$):

Which of the following statements is not true?

$A$ cubical box of side $a$ sitting on a rough table-top is pushed horizontally with a gradually increasing force until the box moves. If the force is applied at a height from the table top which is greater than a critical height $H$,the box topples first. If it is applied at a height less than $H$,the box starts sliding first. Then,the coefficient of friction between the box and the table top is

$A$ cold soft drink is kept on a balance. When the cap is opened,the weight reading on the balance:

$A$ solid ball is suspended from the ceiling of a motor car through a light string. $A$ transverse pulse travels at the speed $60 \text{ cm/s}$ on the string, when the car is at rest. When the car accelerates on a horizontal road, the speed of the pulse is $66 \text{ cm/s}$. The acceleration of the car is nearly $\left(g=10 \text{ m/s}^2\right)$ (in $\text{ m/s}^2$)