A car of mass m starts from rest and  accelerates so that the instantaneous power delivered to the car has a constant magnitude P_o. The instantaneous velocity of this car is proportional to

1. t₂P₀

2. t^1/2

3. t^–1/2

4. t / √m

The potential energy of a system increases if the work is done

(1) by the system against a conservative force 

(2) by the system against a nonconservative force

(3) upon the system by a conservative force

(4) upon the system by a nonconservative force

A ball moving with velocity $2<mspace\; width="1em"></mspace>m{s}^{-1}$ collides head on with another stationery ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in $m{s}^{-1}$) after collision will be 

(a)0,1                                                (b)1,1

(c)1,0.5                                             (d)0,2 

A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is v, the power delivered to the particle is 

(1) $\frac{{\mathrm{Mv}}^2}{\mathrm{T}}$                                 

(2) $\frac{1}{2}\frac{{\mathrm{Mv}}^2}{{\mathrm{T}}^2}$

(3) $\frac{{\mathrm{Mv}}^2}{{\mathrm{T}}^2}$                                   

(4) $\frac{1}{2}\frac{{\mathrm{Mv}}^2}{\mathrm{T}}$

A body of mass 1 kg is thrown upwards with a velocity of $20$ ${\mathrm{ms}}^{-1}.$ It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? $\left(\mathrm{g}=10\right)$ ${\mathrm{ms}}^{-2}$

1. 20 J

2. 30 J

3. 40 J

4. 10 J

The points of maximum and minimum attraction in the curve between potential energy (U) and distance (r) of a diatomic molecules are respectively -

(a) Sand R

(b) T and S

(c) R and S

(d) S and T

K is the force constant of a spring. The work done in increasing its extension from $l_1$ to $l_2$ will be

(1) $K\left(l_2-l_1\right)$                             

(2) $\frac{K}{2}\left(l_2+l_1\right)$

(3) $K\left(l_2^2-l_1^2\right)$                           

(4) $\frac{K}{2}\left(l_2^2-l_1^2\right)$

A body of mass $m_1$ moving with uniform velocity of 40 m/s collides with another mass $m_2$ at rest and then the two together begin to move with uniform velocity of 30 m/s. The ratio of their masses $\frac{m_1}{m_2}$ is

(1) 0.75

(2) 1.33

(3) 3.0

(4) 4.0

A ball of mass m moving with a speed u undergoes a head-on elastic collision with a ball of mass nm initially at rest. The fraction of initial energy transferred to the heavier ball is

(1) $\frac{n}{1+n}$

(2) $\frac{n}{{(1+n)}^2}$

(3) $\frac{2n}{{(1+n)}^2}$

(4) $\frac{4n}{{(1+n)}^2}$

A sphere of mass m moving horizontally with velocity $v_0$ collides against a pendulum bob of mass m. If the two masses stick together after the collision, then the maximum height attained is

(1) $\frac{v_0^2}{2g}$

(2) $\frac{v_0^2}{4g}$

(3) $\frac{v_0^2}{6g}$

(4) $\frac{v_0^2}{8g}$