Work, Energy and Power

A cone filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. What must be the maximum period of revolution?

• 2 sec

• 4 sec

• 1 sec

• 6 sec

A car and a container, moving with equal kinetic energies are stopped by applying a negative acceleration. Then

• container will move less distance before being stopped

• both will become stationary after moving some distance

• car will move less distance before being stopped

• none of the above

The momentum of two masses m₁ and m₂ are same. The ratio of their kinetic energies E₁ and E₂ is

• $\sqrt{{\mathrm{m}}_1} : \sqrt{{\mathrm{m}}_2}$

• m₁ : m₂

• m₂ : m₁

• m₁² : m₂² 

n balls each of mass m and velocity v collide with a wall, assume that the collisions are perfectly elastic. The pressure exerted per second on the wall is 

• 3 mnv

• mnv

• 2mnv

• none

The ground state energy of hydrogen atom is -13.6 eV. The kinetic energy of the electron
in this state is

• 27.2 eV

• 13.6 eV

• 6.8 eV

• 3.4 eV

A massless spring of natural length of 0.5 m and spring constant 50 N/m has one end fixed and the other end attached to mass of 250 g. The spring mass system is on a smooth floor. The mass is pulled until the length of the spring is 0.6 and then released from rest. The kinetic energy of the mass when the length of the spring is 0.5 m is

• 0.0176 J

• 2.25 J

• 6.25 J 

• 9 J

A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

• $\frac{\mathrm{L}}{4}$

• 2L

• 4L

• $\frac{\mathrm{L}}{2}$

A spring scale is adjusted to read zero. Particles of mass 1 g fall on the pan of the scale and collide elastically and they rebound upward with the same speed. If the height of fall of particles is 2 m and their rate of collision is 100 particles per second, then the scale reading in grams will be (g =9.8 m/s)?

• 1000 g

• 1100 g

• 1200 g

• 1252 g

A smooth sphere of mass m moving with velocity u directly collides elastically with another sphere of mass M at rest. After collision their final velocities are V and v respectively. The value of v is

• $2\mathrm{u} \frac{\mathrm{M}}{\mathrm{m}}$

• $2\mathrm{u} \frac{\mathrm{m}}{\mathrm{M}}$

• $\frac{2 \mathrm{u}}{1 + {\displaystyle \frac{\mathrm{m}}{\mathrm{M}}}}$

• $\frac{2 \mathrm{u}}{1 + {\displaystyle \frac{\mathrm{M}}{\mathrm{m}}}}$

A water film is made between two 10 cm long straight wires and at a distance of 0.5 cm. If distance between the wires is increased by 1 mm, then work done will be (T = 7.2 x 10^-2N/m)

• 7.22 × 10^-6 J

• 1.44 × 10^-5 J

• 2.88 × 10^-5 J

• 5.76 × 10^-5 J