if the radius of the earth were to shrink by 1 percent with

If the radius of the earth were to shrink by $$1\% ,$$ with its mass remaining the same, the acceleration due to gravity on the earth’s surface would

A. decrease by $$1\% $$

B. decrease by $$2\% $$

C. increase by $$1\% $$

D. increase by $$2\% $$

Answer : increase by $$2\% $$

Solution :
$${\text{As}}\,\,g = \frac{{{\text{ }}GM{\text{ }}}}{{{R^2}}}$$
when radius is reduced by $$1\% $$ then
$$\eqalign{ & R' = R - \frac{R}{{100}} = .99\,R, \cr & {\text{so,}}\,g' = \frac{{GM}}{{{{\left( {.99\,R} \right)}^2}}} = 1.02\frac{{GM}}{{{R^2}}} \cr & \Rightarrow \% \,{\text{increase}}\, = 2\% \cr} $$

Releted MCQ Question on
Basic Physics >> Gravitation

Releted Question 1

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

A. Decrease

B. Remain unchanged

C. Increase

D. Be zero

View Answer

Releted Question 2

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

A. $$\frac{1}{2}\,mgR$$

B. $$2\,mgR$$

C. $$mgR$$

D. $$\frac{1}{4}mgR$$

View Answer

Releted Question 3

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A. $$64.5$$

B. $$129$$

C. $$182.5$$

D. $$730$$

View Answer

Releted Question 4

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$ Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$ will approximately be-

A. $$\frac{1}{2}\,hr$$

B. $$1 \,hr$$

C. $$2 \,hr$$

D. $$4 \,hr$$

View Answer

If the radius of the earth were to shrink by $$1\% ,$$ with its mass remaining the same, the acceleration due to gravity on the earth’s surface would

Releted MCQ Question on
Basic Physics >> Gravitation

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$ Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$ will approximately be-

Practice More Releted MCQ Question on
Gravitation

Practice More MCQ Question on Physics Section

If the radius of the earth were to shrink by $$1\% ,$$ with its mass remaining the same, the acceleration due to gravity on the earth’s surface would

Releted MCQ Question on Basic Physics >> Gravitation

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$ Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$ will approximately be-

Practice More Releted MCQ Question on Gravitation

Practice More MCQ Question on Physics Section

Releted MCQ Question on
Basic Physics >> Gravitation

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Gravitation