Work, Energy and Power

When two springs A and B with force constants k_A and k_B are stretched by the same force, then the respective ratio of the work done on them is 

• k_B : k_A

• k_A : k_B

• k_A : k_B : 1

• $\sqrt{{\mathrm{k}}_{\mathrm{B}}} : \sqrt{{\mathrm{k}}_{\mathrm{A}}}$

In elastic collision

• both momentum and kinetic energy are conserved

• neither momentum nor kinetic energy is conserved

• only momentum is conserved

• only kinetic energy is conserved

A spring stores 1 J of energy for a compression of 1 mm. The additional work to be done to compress it further by 1 mm is

• 1 J

• 2 J

• 3 J

• 4 J

A crate is pushed horizontally with 100 N across a 5 m floor. If the frictional force between the crate and the floor is 40 N, then the kinetic energy gained by the crate is

• 200 J

• 240 J

• 250 J

• 300 J

An engine pumps out water continuously through a hose with a velocity v. If m is the mass per unit length of the water jet, the rate at which the kinetic energy is imparted to water is

• $\frac{1}{2} {\mathrm{mv}}^2$

• $\frac{1}{2} {\mathrm{mv}}^3$

• $\frac{1}{2} {\mathrm{m}}^2{\mathrm{v}}^2$

• mv³

The radiating power of a linear antenna of length l for a wave of wavelength is proportional to

• $\frac{\mathrm{l}}{\mathrm{\lambda }}$

• $\frac{{\mathrm{l}}^2}{{\mathrm{\lambda }}^2}$

• $\frac{1}{{\mathrm{\lambda }}^2}$

• $\frac{1}{\sqrt{\mathrm{\lambda }}}$

The position of a particle of mass 4 g, acted upon by a constant force is given by x = 4 t², where x is in metre and t in second. The work done during the first 2 s is

• 128 mJ

• 512 mJ

• 576 mJ

• 144 mJ

The shape of the curve representing the relation between the speed and kinetic energy of a moving object is

• parabola

• ellipse

• straight line with positive slope

• straight line with negative slope

A force $\left(4\hat{\mathrm{i}} + \hat{\mathrm{j}} - 2\hat{\mathrm{k}}\right)$ N acting on a body maintains its velocity at $\left(2\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}\right)$ ms^-1. The power exerted is

• 4 W

• 5 W

• 2 W

• 8 W

Energy required to break one bond in DNA is

• 10^-10 J

• 10^-18 J

• 10^-7 J

• 10^-20 J