Laws of Motion

A maximum of $3N$force can be applied onablock, down the incline, thatwould stillnotmove the block which isplaced on a rough inclined plane as shown in the figure. The maximum external force up the inclined plane that…

A light string passing over a smooth light pulley connects two blocks of masses $\mathrm{m}_1$ and $\mathrm{m}_2$ (where $m_2 \gt m_1$). If the acceleration of the system is $\frac{\mathrm{g}}{\sqrt{2}}$, then the ratio…

At any instant the velocity of a particle of mass $500 \mathrm{~g}$ is $\left(2 t \hat{i}+3 t^2 \hat{j}\right) \mathrm{ms}^{-1}$. If the force acting on the particle at $t=1 s$ is $(\hat{i}+x \hat{j}) N$. Then the value…

A particle of mass $m$ is projected with velocity $v$ at an angle $\theta$ with the horizontal. At its highest point, it explodes into two pieces of equal mass, one of the piece continue to move on the original…

What will be the acceleration due to gravity at a depth $d$, where $g$ is acceleration due to gravity on the surface of earth?

A ball of mass $0.2 \mathrm{~kg}$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2 \mathrm{~m}$ while applying the force and the ball goes upto $2 \mathrm{~m}$ height further, find the…

A body of mass $2 \mathrm{~kg}$ is placed on a horizontal surface having kinetic friction 0.4 and static friction $0.5 .$ If the force applied on the body is $2.5 \mathrm{~N},$ then the frictional force acting on the…

The coefficient of friction between the rubber tyres and the road wayis $0.25 .$ The maximum speed with which a car can be driven round a curve of radius $20 \mathrm{~m}$ without skidding is $\left(\mathrm{g}=9.8…

The upper half of an inclined plane with inclination $\phi$ is perfectlysmooth while the lower halfis rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for…

The force on a body of mass $1 \text{kg}$ is $(20 \vec{i}+10 \vec{j}) N$. If it starts from rest, then the position of the body at time $t=2 s,$ is

A body of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t=0$, a force $F=at$ acts in the same direction on the moving particle during time interval of $T$. So that its momentum changes from…

A person with his hand in his pocket is skating on ice at the rate of $10 \mathrm{~m} / \mathrm{s}$ and describes a circle of radius $50 \mathrm{~m}$. What is his inclination to vertical: $\left(\mathrm{g}=10…