A cord is used to vertically lower a block of mass m by a distance d at a constant downward acceleration of $\frac{\text{'}\mathrm{g}\text{'}}{4}$. The work done by the chord on the block will be:

1.  $\frac{3}{4}$mgd

2.  -$\frac{3}{4}$mgd

3.  $\frac{1}{4}$mgd

4.   -$\frac{1}{4}$mgd

An engine pumps liquid of density d continuously through a pipe of cross-sectional area A. If the speed with which liquid passes through the pipe is v, then the rate at which kinetic energy is being imparted to the liquid by the pump is: 

The work done in increasing the length of a massless spring from its natural length 15 cm to 15.1 cm is 20 J. Work done in increasing the length from 15.1 cm to 15.2 cm will be:

A body of mass m moving at a certain speed suffers a perfectly inelastic collision with a body of mass M at rest. The ratio of the final kinetic energy of the system to the initial kinetic energy will be:

Work done by frictional force during the walking of a man is:
1. positive
2. negative
3. zero
4. maybe positive or negative

A particle is moving such that the potential energy U varies with position in metre as U (x) = ($4{\mathrm{x}}^2$ - 2x + 50) J. The particle will be in equilibrium at: 
1. x = 25 cm
2. x = 2.5 cm
3. x = 25 m
4. x = 2.5 m

Select the incorrect statement about potential energy:

                       
1. \(v\sqrt{\dfrac{m}{k}}\)

2. \(v\sqrt{\dfrac{2m}{k}}\)

3. \(m\sqrt{\dfrac{v}{2k}}\)

4. \(v\sqrt{\dfrac{m}{2k}}\)