In the shown diagram mass of A is m and that of B is 2 m. All the surfaces are smooth. System is released from rest with spring unstretched. Then, the maximum extension $\left(x_m\right)$ in spring will be:

An equilateral prism of mass $m$ rests on a rough horizontal surface with coefficient of friction $\mu .$ A horizontal force $F$ is applied on the prism as shown in figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, the minimum force required to topple the prism is

A particle of mass $m$ is released from rest at point $A$ in the figure falling freely under gravity parallel to the vertical $Y-axis.$ The magnitude of angular momentum of particle about point $O$ when it reaches $B$ is (where $OA=b$ and $AB=h)$

A current carrying squre loop is placed near an infinitely long current carrying wire as shown in figure . The loop torque acting on the loop is

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $\omega$, Two objects, each of mass m, are attached gently to the opposite ends of a diameter of the ring. The wheel now rotates with an angular velocity $\omega =$

A vehicle of mass $M$ is moving on a rough horizontal road with a momentum P If the coefficient of friction between the tyres and the road is $\mu$ is then the stopping distance is .

The moment of inertia of a uniform rod of length $2l$ and mass $m$ about an axis $xy$ passing through its centre and inclined at an angle $\alpha$ is

A particle projected with velocity u at angle $\theta$ with horizontal at t=0. What is the magnitude of change in the velocity of the particle when it is at maximum height?

What would be the projections velocity of a satellite so that intersteller (interspace with no gravitation) velocity of the satellite becomes the orbital velocity when it is in the orbit at height of $10R$ from earth's surface, where $R$ is the radius of the earth?

A ball strikes a wall with a velocity $\vec{u}$ at an angle $\theta$ with the normal to the wall surface. and rebounds from it at an angle $\beta$ with the surface. Then