CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A tunnel is dug across the earth of mass M and radius R at a distance R/2 from the centre O of the Earth as shown. A body is released from rest from one end of the smooth tunnel. The velocity acquired by the body when it reaches the centre C of the tunnel is


A
3GM2R
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3GM4R
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
3GM8R
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
3GM16R
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 3GM4R
Given,
Velocity at point A, vA=0

Let, the velocity acquired at point C be v.

Applying energy conservation principle between points A and C, we have:


P.EA+K.EA=P.EC+K.EC

Substituting the values, we get

GMmR+0=GMmR3[32R212(R2)2]+12mv2

GMmR=118GMmR+12mv2

12mv2=38GMmR

v=3GM4R

Hence, option (b) is the correct answer.
Why this Question:
This question will help students to understand the application of energy conservation principle inside a tunnel.

flag
Suggest Corrections
thumbs-up
7
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon