Escape velocity of a rocket is 11.2 km/sec. It is released at an angle of 45^°. Its escape velocity is

• 11.2 m/sec

• 11.2$\sqrt{2}$ km/sec

• 11.2 km/sec

• 22.3 km/sec

What is the dimensional formula for the gravitational constant?

• [ M^-1 L³ T^-2 ]

• [ M^-1 L³ T^-1 ]

• [ M^-2 L³ T^-2 ]

• [ M^-2 L^-1 T³ ]

The equivalent resistance between A and C of the given circuit, is

• 8 Ω

• $\frac{32}{14} \mathrm{\Omega }$

• $\frac{4}{3}$Ω

• $\frac{8}{3}$Ω

Assertion:  At pole value of acceleration due to gravity (g) is greater than that of equator. 

Reason:  Earth rotates on its axis in addition to revolving round the sun.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true and reason is not the correct expalnation of assertion.

• If assertion is true but reason is false.

• If assertion is false and reason is true.

Assertion: The time period of revolution of a satellite around a planet is directly proportional to the radius of the orbit of the satellite.

Reason:  Artificial satellite do not follow Kepler's laws of planatary motion.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion is true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If assertion is false but reason is true.

A body weighs 200 N at the surface of earth. If it be placed in an artificial satellite revolving at height where acceleration due to gravity is half of that at earth's surface. It will weigh

• 100N

• 200N

• 400N

• Zero

In planetary motion, the areal velocity of position vector of a planet depends on angular velocity ($\mathrm{\omega }$) and distance of the planet from the sun (r). If so the correct relation for areal velocity is

• $\frac{\mathrm{dA}}{\mathrm{dt}} \propto \mathrm{\omega r}$

• $\frac{\mathrm{dA}}{\mathrm{dt}} \propto {\mathrm{\omega }}^2\mathrm{r}$

• $\frac{\mathrm{dA}}{\mathrm{dt}} \propto {\mathrm{\omega r}}^2$

• $\frac{\mathrm{dA}}{\mathrm{dt}} \propto \sqrt{\mathrm{\omega r}}$

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

An artificial satellite revolves around the earth in a circular orbit with a speed v. If m is the mass of the satellite, its total energy is

• $\frac{1}{2}$mv²

• $\frac{-1}{2}$mv²

• -mv²

• $\frac{3}{2}$mv²