A pump ejects 12,000 kg of water at a speed of 4 m/s in 40 s. The average rate at which the pump is working is:

1.  0.24 kW

2.  2.4 W

3.  2.4 kW

4.  24 W

A block of mass 2 kg moving with a velocity of 10 m/s on a smooth surface hits a spring of force constant $80\times {10}^3$ N/m as shown. The maximum compression in the spring will be:
               

A body is displaced from (0, 0) to (1m, 1m) along the path x=y by a force $F=\left(x^2\hat{j}+y\hat{i}\right)N$. The work done by this force will be :

1. $\frac{4}{3}J$

2. $\frac{5}{6}J$

3. $\frac{3}{2}J$

4. $\frac{7}{5}J$

A block of mass m initially at rest, is dropped from a height h onto a spring of force constant k. If the maximum compression in the spring is x, then:     
         

1. $mgh=\frac{1}{2}k{x}^2$

2. $mg(h+x)=\frac{1}{2}k{x}^2$

3. $mgh=\frac{1}{2}k{(x+h)}^2$

4. $mg(h+x)=\frac{1}{2}k{(x+h)}^2$

What is the work done by gravity on block A in 2 seconds after the blocks are released? (Pulley is light)

1.  240 J

2.  200 J

3.  120 J

4.  24 J

A weight 'mg' is suspended from a spring. The energy stored in the spring is U. The elongation in the spring is:

1.  $\frac{2\mathrm{U}}{\mathrm{mg}}$

2.  $\frac{\mathrm{U}}{\mathrm{mg}}$

3.  $\frac{\sqrt{2}\mathrm{U}}{\mathrm{mg}}$

4.  $\frac{\mathrm{U}}{\sqrt{2}\mathrm{mg}}$

In the given figure, a man pulls the mass m with the help of a rope. Work done by the man against gravity when mass is lifted by 0.5 m is: (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

     
1. 50 J
2. 100 J
3. 25 J
4. Zero

A block is carried slowly up an inclined plane. If ${\mathrm{W}}_{\mathrm{f}}$ is work done by the friction, ${\mathrm{W}}_{\mathrm{N}}$ is work done by the reaction force, ${\mathrm{W}}_{\mathrm{g}}$ is work done by the gravitational force and ${\mathrm{W}}_{\mathrm{ex}}$ is the work done by an external force, then choose the correct relation(s):

1.  ${\mathrm{W}}_{\mathrm{N}}$ $+$ ${\mathrm{W}}_{\mathrm{f}}$ $+$ ${\mathrm{W}}_{\mathrm{g}}$ $+$ ${\mathrm{W}}_{\mathrm{ex}}$ $=$ $0$

2.  ${\mathrm{W}}_{\mathrm{N}}$ = 0

3.  ${\mathrm{W}}_{\mathrm{ex}}$ $+$ $$ ${\mathrm{W}}_{\mathrm{f}}$ $=$ $-{\mathrm{W}}_{\mathrm{g}}$

4.  All of these

The principle of conservation of energy implies that:

1.  the total mechanical energy is conserved.

2.  the total kinetic energy is conserved.

3.  the total potential energy is conserved.

4.  the sum of all types of energies is conserved.