A body of mass 3 kg is under a constant force that causes a displacement s in metres in it, given by the relation $s=\frac{1}{3}{t}^2$, where t is in seconds. Work done by the force in 2 s is

(1) $\frac{5}{19} J$

(2) $\frac{3}{8} J$

(3) $\frac{8}{3} J$

(4) $\frac{19}{5} J$

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm the potential energy stored in it is

(1) 4 U

(2) 8 U

(3) 16 U

(4) $\frac{U}{4}$

A body of mass 1 kg is thrown upwards with a velocity 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? (g = 10 ${\mathrm{ms}}^{-1}$)

(1) 30 J

(2) 40 J

(3) 10 J

(4) 20 J

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

(1) upon the system by a conservative force.

(2) upon the system by a non-conservative force.

(3) by the system against a conservative force.

(4) by the system against a non-conservative force.

A uniform force of $(3\hat{i}+\hat{j})$ newton acts on a particle of mass 2 kg. Hence the particle is displaced from position $(2\hat{i}+\hat{k})$ m to position $(4\hat{i}+3\hat{j}-\hat{k})$ m. The work done by the force on the particle is 

(1) 9 J

(2) 6 J

(3) 13 J

(4) 15 J

A block of mass 10 kg, moving in x direction with a constant speed of 10 m$s^{-1}$, is subjected ot a retarding force, F = 0.1 x J$m^{-1}$ during its travel from x = 20 to 30 m. Its final K.E. will be

(1) 450 J

(2) 275 J

(3) 250 J

(4) 475 J

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s, Take g constant with a value 10 $m/s^2$. The work done by the (i) gravitational force and the (ii) resistive force  of air is

(1) (i) 1.25 J      (ii) -8.25 J

(2) (i) 100 J       (ii) 8.75 J

(3) (i) 10 J         (ii) -8.75 J

(4) (i) -10 J        (ii) -8.25 J

A moving block having mass m, collides with another stationary block having mass 4 m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of the coefficient of restitution (e) will be 

(1) 0.8

(2) 0.25

(3) 0.5

(4) 0.4

A force F acting on an object varies with distance x as shown here

The force is in Newton and x in meters. The work done by the force in moving the object from x = 0 to x = 6 m is

(1) 18.0 J

(2) 13.5 J

(3) 4.5 J

(4) 9.0 J

A mass of 0.5 kg moving with a speed of 1.5 m$s^{-1}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N$m^{-1}$. The maximum compression of the spring would be

(1) 0.12 m

(2) 1.5 m

(3) 0.5 m

(4) 0.15 m