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 satellite is in a circular orbit round the earth at an altitude R above the earth's surface,where R is the radius of the earth. If g is the acceleration due to gravity on the surface of the earth the speed of the satellite is

• $\sqrt{2\mathrm{Rg}}$

• $\sqrt{\mathrm{Rg}}$

• $\sqrt{\mathrm{Rg}/2}$

• $\sqrt{\mathrm{Rg}/4}$

The moment of inertia of a ring about one of its diameter is I. What will be its moment of inertia about a tangent parallel to the diameter?

• $\frac{4}{3}$ I

• 2 I

• $\frac{3}{2}$ I

• 3 I

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 disc, initially at rest, starts rotating about its own axis, with a constant angular acceleration of 0.2 rad/s². The time taken by the disc to rotate by 10 rad is (in second)

• 7.07

• 10

• 14.14

• 100

Two satellites S₁ and S₂ revolve round a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 h and 8 h respectively. The radius of the orbit of S₁ is 10⁴ km. The speed of S₂ relative to S₁ when they are closest, in km/h is

• 10⁴ $\mathrm{\pi }$

• 2 × 10⁴ $\mathrm{\pi }$

• 10⁴ $\frac{\mathrm{\pi }}{2}$

• 4 × 10⁴ $\mathrm{\pi }$

A disc of a siren containing 60 holes rotates at a constant speed of 360 rpm. The emitted sound is in unison with a tuning fork of frequency

• 10 Hz

• 360 Hz

• 216 Hz

• 60 Hz

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 circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then the relation between the moments of inertia I_X and I_Y is

• I_Y = 321_X

• I_Y = 161_X

• I_Y = I_X

• I_Y = 641_X

A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/s. The tension in the string is 6 N, when the stone is a

• top of the circle

• bottom of the circle

• halfway down

• None of the above