$A$ sphere is placed rotating with its centre initially at rest in a corner as shown in figures $(a)$ and $(b)$. The coefficient of friction between all surfaces and the sphere is $\mu = \frac{1}{3}$. Find the ratio of the frictional force $\frac{f_a}{f_b}$ exerted by the ground in situations $(a)$ and $(b)$.

$A$ person with a machine gun can fire $50 \ g$ bullets with a velocity of $240 \ m/s$. $A$ $60 \ kg$ tiger moves towards him with a velocity of $12 \ m/s$. In order to stop the tiger in its track,the number of bullets the person must fire towards the tiger is:

When a body moves with some friction on a surface,

Four blocks $A, B, C$ and $D$ of masses $6 \,kg, 3 \,kg, 6 \,kg$ and $1 \,kg$ respectively are connected by light strings passing over frictionless pulleys as shown in the figure. The strings $P$ and $Q$ are horizontal. The coefficient of friction between the horizontal surface and the block $B$ is $0.2$ and the blocks $A$ and $B$ move together. If the system is released from rest, then the tension in the string $Q$ is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,N$)

At time $t=0$, a force $F=\alpha t$, where $t$ is time in seconds, is applied to a body of mass $1 \text{ kg}$, resting on a smooth horizontal plane. If the direction of the force makes an angle of $45^{\circ}$ with the horizontal, then the velocity of the body at the moment of its breaking off the plane is

Which of the following is not a fundamental force in nature?