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 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 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: