If the mass of sun were ten times smaller and gravitational constant G were ten times larger in magnitudes-

(a) Walking on ground would became more difficult.

(b) The acceleration due to gravity on earth will not change.

(c) Raindrops will fall much faster.

(d) Airplanes will have to travel much faster.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer-a, c, d

Explanation- G’=10G

Consider the diagram

Force on the objects due to the earth = $\frac{G^{\text{'}}Mm}{R^2}=\frac{10GMm}{R^2}$

= (10g)m= 10mg

Force on the objects due to the sun F= $\frac{GM\text{'}m}{r^2}=\frac{GMm}{10r^2}$

As r>>R  so F will be very small

So effect of sun will be neglected

Now g’=10g

Hence weight of person =10mg

So gravity pull on the person will increase, due to it walking on ground would be more difficult

Critical velocity V_c is proportional to g

So V_{c $\propto g$}

V’>g

V_c’>V_c hence rain will fall faster. To overcome the increased gravitational force of the earth the aeroplane will have to travel much faster.

<p>This is a Multiple Choice Questions as classified in NCERT Exemplar</p><p><strong>Answer-a, c, d</strong></p><p><strong>Explanation-</strong> G’=10G</p><p>Consider the diagram</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745473921phpmoHpNb_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745473921phpmoHpNb.jpeg" alt="" width="150" height="123"></picture></div></div><p>Force on the objects due to the earth =<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msup> <mrow> <mrow> <mi>G</mi> </mrow> </mrow> <mrow> <mrow> <mi>'</mi> </mrow> </mrow> </msup> <mi>M</mi> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>10</mn> <mi>G</mi> <mi>M</mi> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> </span></p><p>= (10g)m= 10mg</p><p>Force on the objects due to the sun F=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>G</mi> <mi>M</mi> <mi>'</mi> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>G</mi> <mi>M</mi> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>10</mn> <msup> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> </span></p><p>As r&gt;&gt;R&nbsp; so F will be very small</p><p>So effect of sun will be neglected</p><p>Now g’=10g</p><p>Hence weight of person =10mg</p><p>So gravity pull on the person will increase, due to it walking on ground would be more difficult</p><p>Critical velocity V_c is proportional to g</p><p>So V_{c<span contenteditable="false"> <math> <mo>∝</mo> <mi>g</mi> </math> </span>}</p><p>V’&gt;g</p><p>V_c’&gt;V_c hence rain will fall faster. To overcome the increased gravitational force of the earth the aeroplane will have to travel much faster.</p>

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