Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

If the radius of earth’s orbit is made $¼$ , calculate the duration of a year on earth.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

T / 6

T / 4

T / 8

T

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

If the radius of earth’s orbit is made

¼

, the duration of a year will be

T / 8

.
From Kepler’s laws of planetary motion we have

T^{2} \propto r^{3}

where T is the time period of revolution of the planet and r is the mean distance between the planet and the sun.

{(\frac{T_{1}}{T})}^{2} = {(\frac{r_{1}}{r})}^{3}

Given, The time period of revolution when the radius is reduced to

¼

of its initial value, be

T

and the reduced radius be

r,

then

T_{1} = 1 year

{4 r}_{2} = r_{1}

{T_{1}}^{2} = ({\frac{1}{2})}^{3} T

\Rightarrow T_{1} = ({\frac{1}{4})}^{\frac{3}{2}} T

\Rightarrow T_{1} = \frac{T}{8}

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE