1
MHT CET 2023 11th May Morning Shift
+1
-0

The radius of earth is $$6400 \mathrm{~km}$$ and acceleration due to gravity $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$. For the weight of body of mass $$5 \mathrm{~kg}$$ to be zero on equator, rotational velocity of the earth must be (in $$\mathrm{rad} / \mathrm{s}$$ )

A
$$\frac{1}{80}$$
B
$$\frac{1}{400}$$
C
$$\frac{1}{800}$$
D
$$\frac{1}{1600}$$
2
MHT CET 2023 11th May Morning Shift
+1
-0

A body of mass '$$\mathrm{m}$$' kg starts falling from a distance 3R above earth's surface. When it reaches a distance '$$R$$' above the surface of the earth of radius '$$R$$' and Mass '$$M$$', then its kinetic energy is

A
$$\frac{2}{3} \frac{\mathrm{GMm}}{\mathrm{R}}$$
B
$$\frac{1}{3} \frac{\mathrm{GMm}}{\mathrm{R}}$$
C
$$\frac{1}{2} \frac{\mathrm{GMm}}{\mathrm{R}}$$
D
$$\frac{1}{4} \frac{\mathrm{GMm}}{\mathrm{R}}$$
3
MHT CET 2023 10th May Evening Shift
+1
-0

A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height reached by the satellite is ( $$R$$ = radius of earth)

A
$$\mathrm{R}$$
B
$$\frac{R}{2}$$
C
$$\frac{R}{3}$$
D
$$\frac{\mathrm{R}}{4}$$
4
MHT CET 2023 10th May Evening Shift
+1
-0

A system consists of three particles each of mass '$$m_1$$' placed at the corners of an equilateral triangle of side '$$\frac{\mathrm{L}}{3}$$', A particle of mass '$$\mathrm{m}_2$$' is placed at the mid point of any one side of the triangle. Due to the system of particles, the force acting on $$\mathrm{m}_2$$ is

A
$$\frac{3 \mathrm{Gm}_1 \mathrm{~m}_2}{\mathrm{~L}^2}$$
B
$$\frac{6 \mathrm{Gm}_1 \mathrm{~m}_2}{\mathrm{~L}^2}$$
C
$$\frac{9 \mathrm{Gm}_1 \mathrm{~m}_2}{\mathrm{~L}^2}$$
D
$$\frac{12 \mathrm{Gm}_1 \mathrm{~m}_2}{\mathrm{~L}^2}$$
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