Work, Energy and Power

If we increase kinetic energy of a body 300%, then per cent increase in its momentum is

• 50%

• 300%

• 100%

• 150%

A particle of mass M and charge Q moving with velocity v describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field, when the particle completes one full circle, is

• $\left(\frac{\mathrm{M} {\mathrm{v}}^2}{\mathrm{R}}\right) 2\mathrm{\pi R}$

• zero

• $\mathrm{BQ} 2\mathrm{\pi R}$

• $\mathrm{BQv} 2\mathrm{\pi R}$

A particle of mass 100 g is thrown vertically upward with a speed of 5 m/s. The work done by the force of gravity during the time the particle goes up is 

• -0.5 J

• -1.25 J

• 1.25 J

• 0.5 J

One end of a massless spring of constant 100 N /m and natural length 0.5 m is fixed and the other end is connected to a particle of mass 0.5 kg lying on a frictionless horizontal table. The spring remains horizontal. If the mass is made to rotate at angular velocity of 2 rad/s, then elongation of spring is

• 0.1 m

• 10 cm

• 1 cm

• 0.01 cm

A block of mass 2 kg is pushed against a  rough vertical wall with a force of 40 N, coefficient of static friction being 0.5. Another horizontal force of 15 N, is applied
on the block in a direction parallel to the wall. If the block will move, then its direction would be

• 15^o with 15 N force

• 53^o with 15 N force

• 45^o with 15 N force 

• 75^o with 15N force

Two wires are stretched through same distance. The force constant ofsecond wire is half as that of the first wire. The ratio of work done to stretch first wire and second wire will be

• 2 : 1

• 1 : 2

• 3 : 1

• 1 : 3

A light string passes over a frictionless pulley. To one of its ends a mass of 8 kg is attached. To its other end two masses of 7 kg each are attached. The acceleration of the system will be

• 10.2 g

• 5.10 g

• 20.36 g

• 0.27 g

A sphere of mass m moving with velocity v hits inelastically with another stationary sphere of same mass. The ratio of their final velocities will be (in terms of e)

• $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2} = \frac{1 + \mathrm{e}}{1 - \mathrm{e}}$

• $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2} = \frac{1 - \mathrm{e}}{1 + \mathrm{e}}$

• $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2} = \frac{1 + \mathrm{e}}{2}$

• $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2} = \frac{1 - \mathrm{e}}{2}$

A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinetic energy is lost by impact, the value of coefficient of restitution is

• 1 / 2√2

• 1 / √3

• 1 / √2

• √3 / 2

A transformer with efficiency 80% works at 4 kW and 100 V. If the secondary voltage is 200 V, then the primary and secondary currents are respectively

• 40 A and 16 A

• 16 A and 40 A

• 20 A and 40 A

• 40 A and 20 A