Physics Laws of Motion

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 10μF capacitor is fully charged to a potential difference of 50 V. After removing the source voltage, it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20 V. The capacitance of the second capacitor 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: