Overview

Two blocks (m = 0.5kg and M = 4.5kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is 3/7. Then the maximum horizontal force that can be applied on the block so that blocks move together is ---------N. (Round off to the Nearest Integer) [ Take g as 9.8 ms^-2]

A modern grand - prix racing car of mass m is traveling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static between the tyres and the track is µs, then the magnitude of negative lift F acting downwards on the car is : (Assume forces on the four tyres are identical and g = acceleration due to gravity)

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv² where v is it speed. The maximum height attained by the ball is:

A particle moving in the xy plane experiences a velocity dependent force F = k(vᵧî + vₓĵ), where vₓ and vᵧ are the x and y components of its velocity v. If a is the acceleration of the particle, then which of the following statements is true for the particle?

A block starts moving up an inclined plane of inclination ${30}^{\circ }$ with an initial velocity of $v_0$

It comes back to its initial position with velocity $\frac{v_0}{2}$   . The value of the coefficient $\frac{v_0}{2}$ kinetic friction between the block and the inclined plane is close to $\frac{1}{1000}$ , The nearest integer to ^$I$  is             .

A Tennis ball is released from a height $h$ $$ and after freely falling on a wooden floor it rebounds and reaches height $\frac{h}{2}$ $\frac{}{}$ . The velocity versus height of the ball during its motion may be represented graphically by:

(graphs are drawn schematically and on not to scale)

A particle of mass m is moving along the x-axis with initial velocity uî. It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If sin θ? = √n sin θ? then value of n is

A charge Q is distributed over two concentric conducting thin spherical shells of radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is: