1
BITSAT 2023
+3
-1

A man of mass $m$ starts falling towards a planet of mass $$M$$ and radius $$R$$. As he reaches near to the surface, he realizes that will pass through a small role in the planet. As he enters the role, we sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass $$3 M / 4$$ and a point mass $$M / 4$$ at the centre. Change in the force of gravity experienced by the man is

A
$$\frac{3}{4} \frac{G M m}{R^2}$$
B
0
C
$$\frac{1}{3} \frac{G M m}{R^2}$$
D
$$\frac{4}{3} \frac{G M m}{R^2}$$
2
BITSAT 2022
+3
-1

What will be the acceleration due to gravity at a depth d, where g is acceleration due to gravity on the surface of earth?

A
$${g \over {{{\left[ {1 + {d \over R}} \right]}^2}}}$$
B
$$g\left[ {1 - {{2d} \over R}} \right]$$
C
$${g \over {{{\left[ {1 - {d \over R}} \right]}^2}}}$$
D
$$g\left[ {1 - {d \over R}} \right]$$
3
BITSAT 2021
+3
-1

From a solid sphere of mass M and radius R, a spherical portion of radius $${R \over 2}$$ is removed as shown in the figure.

Taking gravitational potential V = 0 at r = $$\infty$$, the potential at the centre of the cavity thus formed is

A
$$- {{GM} \over {2R}}$$
B
$$- {{GM} \over {R}}$$
C
$$- {{2GM} \over {3R}}$$
D
$$- {{2GM} \over {R}}$$
4
BITSAT 2021
+3
-1

If the earth stops rotating about its axis, then what will be the change in the value of g at a place in the equatorial plane? (Radius of earth = 6400 km)

A
3.7 cm/s2
B
9.8 m/s2
C
0
D
3.4 cm/s2
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