1
MHT CET 2022 11th August Evening Shift
+1
-0

The masses and radii of the moon and the earth are $$\mathrm{M_1, R_1}$$ and $$\mathrm{M_2, R_2}$$ respectively. Their centres are at a distance $$\mathrm{d}$$ apart. What should be the minimum speed with which a body of mass '$$m$$' should be projected from a point midway between their centres, so as to escape to infinity?

A
$$\frac{\mathrm{G}\left(\mathrm{M}_1+\mathrm{M}_2\right)}{\mathrm{d}}$$
B
$$\sqrt[2]{\frac{G\left(M_1+M_2\right)}{d}}$$
C
$$\sqrt{\frac{G d}{M_1+M_2}}$$
D
$$\sqrt{\frac{M_1+M_2}{G d}}$$
2
MHT CET 2021 24th September Evening Shift
+1
-0

The average density of the earth is [g is acceleration due to gravity]

A
inversely proportional to g$$^2$$.
B
directly proportional to $$\mathrm{g}$$.
C
inversely proportional to $$\mathrm{g}$$.
D
directly proportional to $$\mathrm{g}^2$$.
3
MHT CET 2021 24th September Evening Shift
+1
-0

The depth from the surface of the earth of radius $$\mathrm{R}$$, at which acceleration due to gravity will be $$60 \%$$ of the value on the earth surface is

A
$$\frac{2 R}{3}$$
B
$$\frac{2 R}{5}$$
C
$$\frac{3 R}{5}$$
D
$$\frac{5 R}{3}$$
4
MHT CET 2021 24th September Evening Shift
+1
-0

Three point masses, each of mass 'm' are kept at the corners of an equilateral triangle of side 'L'. The system rotates about the centre of the triangle without any change in the separation of masses during rotation. The period of rotation is directly proportional to $$\left(\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)$$

A
L
B
$$\mathrm{L}^{1 / 2}$$
C
$$\mathrm{L}^{3 / 2}$$
D
$$\mathrm{L}^{-2}$$
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