wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A small body of mass m moves downward from the hemisphere of radius r if it leaves the hemisphere at a point that is at a distance h below the vertex then:
1078925_2d1380f075e34c30850328b51d4b28ea.png

A
h=r
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
h=r3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
h=r2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
h=2r3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D h=2r3

Given that,

Mass = m

Height = h

Radius = r

Now,

Fc=mgcosθN

When the body leaves the semi sphere

Then, N = 0

Now,

Fc=mgcosθ....(I)

Now,

Fc=mv2r....(II)

From equation (I) and (II)

mgcosθ=mv2r

v2=grcosθ

cosθ=hr

Now, from conservation of energy

Ui+Ki=Uf+Kf

mgr+0=mgh+12mv2

gr=gh+12v2

2gr2gh=grcosθ

2r=r×hr+2h

h=23r

Hence, the height is 23r


1023078_1078925_ans_cb149934dc4142bd9418702f645ac225.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Escape Velocity
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon