Laws of Motion ...

A block of mass m is in contact with the cart as shown in figure

The coefficient of static friction between the block and the cart is . The acceleration of the cart that will prevent the block from falling satisfies

Instantaneous power of constant force acting on a particle moving in a straight line under the action of this force 

In the following figure all surfaces are assumed to be frictionless and pulley is assumed to be ideal. The block 'A' is projected towards the pulley 'P' with an initial velocity $$u_0$$ then select incorrect option

A body is moving in a vertical circle of radius '$$r$$' by a string. If the ratio of maximum to minimum speeds is $$\sqrt{3}:1$$ , the ratio of maximum to minimum tensions in the string is:

A body of mass $$5\ kg$$ undergoes a change in speed from $$30$$ to $$40\ m/s$$. Its momentum would increase by:

A simple pendulum of length $$50 cm$$ is suspended from a fixed point $$O$$ and a nail is fixed at a point $$P$$ which is vertically below $$O$$ at some distance. The bob is released when string is horizontal. The bob reaches lowest position then it describes vertical circle whose centre coincides with point $$P$$. The minimum distance between $$O$$ and $$P$$ is:

A mass $$0.1\ kg$$ is rotated in a vertical circle using the cord of length $$1\ m$$, when the cord makes an angle $$60^0$$ with the vertical, the speed of the mass is $$3\  m/s$$ the resultant  radial acceleration of mass in that position is:

A passenger in a moving train tosses a coin which falls behind him. It means that the motion of the train is

A rubber ball of mass 250 g hits a wall normally with a velocity  $$10 m s^{-1}$$ and bounces back with a velocity of $$8 m s^{-1}$$. The impluse is _______N s.

A stone of mass $$1 kg$$ tied to a light inextensible string of length $$L=\dfrac{10}{3}m$$ is whirling in a circular path of radius $$L$$ in a vertical plane. If the ratio of the maximum tension in the string to the minimum is $$4$$ and if $$g$$ is taken to be $$10 \ m/s^2$$, then speed of stone at the highest point of the circle is