## The change in the value of g at a height h above the surface of earth is the same as at a depth d below the earth…

Q: The change in the value of g at a height h above the surface of earth is the same as at a depth d below the earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?

(a) d = h/2

(b) d = 3h/2

(c) d = 2h

(d) d = h

Ans: (c)

$\displaystyle g_h = g_d$

$\displaystyle g(1-\frac{2h}{R})= g(1-\frac{d}{R})$

d = 2h

## A body is weighed by a spring balance to be 1.000 kg at the north pole….

Q: A body is weighed by a spring balance to be 1.000 kg at the north pole. How much will it weigh at the equator ?

(a) 0.398kg

(b) 0.579kg

(c) 0.235kg

(d) 0.997kg

Ans: (d)

## A mass of 6 ×10^24 kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that

Q: A mass of 6 × 1024 kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 108 ms-1 . What should be the radius of the sphere ?

(a) ≈9mm

(b) ≈9cm

(c) ≈1mm

(d) ≈1m

Ans: (a)
Sol:
$\displaystyle v_e = \sqrt{\frac{2GM}{R}}$
$\displaystyle 3\times 10^8 = \sqrt{\frac{2\times 6.67\times 10^{-11}\times 6 \times 10^{24}}{R}}$
R = 9mm

## The orbital velocity of an artificial satellite in a circular orbit just above the earth’s surface is v….

Q: The orbital velocity of an artificial satellite in a circular orbit just above the earth’s surface is v. For a satellite orbiting at an altitude of half of the earth’s radius, the orbital velocity

(a) $\displaystyle \frac{3}{2} \, v$

(b) $\displaystyle \sqrt{\frac{3}{2} } \, v$

(c) $\displaystyle \sqrt{\frac{2}{3} } \, v$

(d) $\displaystyle \frac{2}{3} \, v$

Ans: (c)

## If the mass of earth were 4 times the present mass, the mass of the moon were half the present mass…

Q: If the mass of earth were 4 times the present mass, the mass of the moon were half the present mass and the moon were revolving round the earth at twice the present distance, the time period of revolution of the moon would be (in days)

(a) 56√2

(b) 28√2

(c) 14√2

(d) 7√2

Ans: (b)