A satellite in a circular orbit of radius R has a period of 4 h. Another satellite with orbital radius 3 R around the same planet will have a period (in hours)

• 16

• 4

• 4√27

• 4√8

The acceleration due to gravity becomes g/2, (g = acceleration due to gravity on the surface of the earth) at a height equal to

• 4R

• R/4

• 2R

• R/2

Two bodies A and B have masses M and m respectively, where M > m and they are at a distance d apart. Equal force is applied to them so that they approach each other. The position where they hit each other is

• nearer to B

• nearer to A

• at equal distance from A and B

• Cannot be predicted

Three particles, each of mass m gram are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm² units will be

• $\frac{3}{4}{\mathrm{ml}}^2$

• 2 ml²

• $\frac{5}{4}{\mathrm{ml}}^2$

• $\frac{3}{2}{\mathrm{ml}}^2$

Two discs of the moment of inertia I₁ and l₂ and angular speeds ω₁ and ω₂, are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate combinedly along the same axis the rotational KE of the system will be

• $\frac{{\mathrm{I}}_1{\mathrm{\omega }}_1 + {\mathrm{I}}_2{\mathrm{\omega }}_2}{2({\mathrm{I}}_1 + {\mathrm{I}}_2)}$

• $\frac{({\mathrm{I}}_1 + {\mathrm{I}}_2)({\mathrm{\omega }}_1 +{\mathrm{\omega }}_2{)}^2}{2}$

• $\frac{({\mathrm{I}}_1{\mathrm{\omega }}_1 + {\mathrm{I}}_2{\mathrm{\omega }}_2{)}^2}{2({\mathrm{I}}_1+ {\mathrm{I}}_2)}$

• None of these

A simple pendulum has a length l and the mass of the bob is m. The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\sqrt{\mathrm{g} + {\displaystyle \frac{\mathrm{qE}}{\mathrm{m}}}}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\sqrt{\mathrm{g} - {\displaystyle \frac{\mathrm{qE}}{\mathrm{m}}}}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\sqrt{{\mathrm{g}}^2 + {\left({\displaystyle \frac{qE}{\mathrm{m}}}\right)}^2}}}$

The unit of Stefan's constant is

• Wm^-2 K^-1

• Wm K^-4

• Wm^-2 K^-4

• Nm^-2 K^-4

A Carnot engine takes heat from a reservoir at 627° C and rejects heat to a sink at 27° C. Its efficiency will be

• 3/5

• 1/3

• 2/3

• 200/209

A tuning fork A produces 4 beats/s with another tuning fork B of frequency 320 Hz. On filling one of the prongs of A, 4 beats/s are again heard when sounded with the same fork B. Then, the frequency of the fork A before the filling is

• 328 Hz

• 316 Hz

• 324 Hz

• 320 Hz

When the length of the vibrating segment of a sonometer wire is increased by 1%, the percentage change in its frequency is

• 100/101

• 99/100

• 1

• 2