AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

‘A’ is a huge planet with uniform mass distribution of mass $M$ , radius $R$ . B is a circular tunnel made in it, concentric with planet. Radius of tunnel is $r$ , $(r = \frac{R}{2})$ cross-sectional diameter is $d (d < < r)$ . C is a small ball of mass $m (m < < M)$ which is moving freely inside the tunnel without friction in a uniform circular motion, take acceleration due to gravity on surface of A as $g$ :

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

If contact force on C is double the gravitational force, its time period is $2 π \sqrt{\frac{R}{g}}$

If contact force on C is double the gravitational force, its time period is $2 π \sqrt{\frac{R}{3 g}}$

If contact force is zero, time period $T$ , radius of tunnel $r$ , then $T \propto r$ .

If contact force is zero, time period $T$ , radius of tunnel $r$ , then T would be independent of $r$ .

answer is A, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

(i) For contact force on C is double the gravitational force

$N + m g^{'} = m r ω^{2}$

$2 m g^{'} + m g^{'} = m r ω^{2}$

$3 g^{'} = r ω^{2}, 3 g (\frac{r}{R}) = r ω^{2}$

$ω = \sqrt{\frac{3 g}{R}}$

$T = \frac{2 π}{ω} = 2 π \sqrt{\frac{R}{3 g}}$

(ii) For N =0, $m g^{'} = m r ω^{2}$
$g \frac{r}{R} = r ω^{2}$ ;

$ω$ is independent of $r$ .

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!