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Physics MCQs for NEET — Practice Questions with Answers

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Two planets have the same average density but their radii are $R_{1}$ and $R_{2}$ . If acceleration due to gravity on these planets be $g_{1}$ and $g_{2}$ respectively, then

$\frac{g_{1}}{g_{2}}$ = $\frac{R_{1}}{R_{2}}$

$\frac{g_{1}}{g_{2}}$ = $\frac{R_{2}}{R_{1}}$

$\frac{g_{1}}{g_{2}}$ = $\frac{{R_{1}}^{2}}{{R_{2}}^{2}}$

$\frac{g_{1}}{g_{2}}$ = $\frac{{R_{1}}^{3}}{{R_{2}}^{3}}$

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Explanation

(a) g= $\frac{4}{3} π ρ G R$ . If $ρ$ = constant then $\frac{g_{1}}{g_{2}}$ = $\frac{R_{1}}{R_{2}}$

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The escape velocity for the earth is 11.2 km/sec. The mass of another planet is 100 times that of the earth and its radius is 4 times that of the earth. The escape velocity for this planet will be

112.0 km/s

5.6 km/s

280.0 km/s

56.0 km/s

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Explanation

(d) $E s c a p e v e l o c i t y v = \sqrt{\frac{2 G M}{R}} \Rightarrow \sqrt{\frac{v_{p}}{v_{e}}} = \sqrt{\frac{M_{p}}{M_{e}} \times \frac{R_{e}}{R_{p}}} \Rightarrow v_{p} = 5 v_{e} = 5 \times 11.2 = 56 k m / s$

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Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If $R_{E}$ is the maximum range of a projectile on the earth’s surface, what is the maximum range on the surface of the moon for the same velocity of projection ?

0.2 $R_{ε}$

2 $R_{ε}$

0.5 $R_{ε}$

5 $R_{ε}$

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Explanation

(d) Range of projectile $R = \frac{u^{2} \sin 2 θ}{g}$

if u and $θ$ are constant then $R \propto \frac{1}{g}$

$\frac{R_{m}}{R_{E}} = \frac{g_{E}}{g_{m}} \Rightarrow \frac{R_{m}}{R_{E}} = \frac{1}{0.2} \Rightarrow R_{m} = \frac{R_{E}}{0.2} \Rightarrow R_{m} = 5 R_{E}$

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The escape velocity on a planet having mass 6 times and radius 2 times as that of earth is

$\sqrt{3} V_{e}$

$3 V_{e}$

$\sqrt{2} V_{e}$

$2 V_{e}$

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Explanation

(a) $\frac{v_{p}}{v_{e}} = \sqrt{\frac{M_{p}}{M_{e}} \times \frac{R_{e}}{R_{p}}} = \sqrt{6 \times \frac{1}{2}} = \sqrt{3} s o, v_{p} = \sqrt{3} v_{e}$

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An iron ball and a wooden ball of the same radius are released from a height ‘h’ in vacuum. The time taken by both of them to reach the ground is

Unequal

Exactly equal

Roughly equal

Zero

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Explanation

b) Time of decent = $\sqrt{\frac{2 h}{g}}$ . In vacuum no other force works except gravity so time period will be exactly equal.

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If density of earth increased 4 times and its radius become half of what it is, our weight will

Be four times its present value

Be doubled

Remain same

Be halved

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Explanation

(b)

$g = \frac{4}{3} πGρR g \propto R ρ g' = 22 W e i g h t w i l l b e d o u b l e d .$

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The escape velocity on earth is 11.2 km/s. On another planet having twice radius and 8 times mass of the earth, the escape velocity will be

3.7 km/s

11.2 km/s

22.4 km/s

43.2 km/s

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Explanation

(c) $\frac{v_{p}}{v_{e}} = \sqrt{\frac{g_{p}}{g_{e}} \times \frac{R_{p}}{R_{e}}} = \sqrt{8 \times \frac{1}{2}} = 2 s o, v_{p} = 2 \times v_{e} = 22.4 k m / s$

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When a body is taken from the equator to the poles, its weight

Remains constant

Increases

Decreases

Increases at N-pole and decreases at S-pole

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Explanation

(b) Because acceleration due to gravity increases

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The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become

5.6 km/s

11.2 km/s (remain unchanged)

22.4 km/s

44.8 km/s

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Explanation

If M becomes double and R becomes half then escape velocity becomes two times

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A body of mass m is taken to the bottom of a deep mine. Then

Its mass increases

Its mass decreases

Its weight increases

Its weight decreases

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Explanation

d) Because acceleration due to gravity decreases

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