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

Figure shows a rod of length 20 cm pivoted near an end and which is made to rotate in a horizontal plane with a constant angular spped. A ball of mass m is suspended by a string also of length 20 cm from the other end of the rod . If the angle θ made by the string with the vertical is 30, find the angular speed of rotation. Take g=10 m/s2

A
4.4 rad/s
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
3.2 rad/s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2.4 rad/s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1.2 rad/s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 4.4 rad/s
Let the angular speed be ω.

As it is clear from the figure, the ball moves in a horizontal circle of radius L+Lsinθ where L=20 cm. Its acceleration is, therefore , ω2(L+Lsinθ) towards the centre.

The forces on the bob are :-
a) the tension T along the string and
b) the weight mg
Resolving the forces along the radius and applying Newton's second law:
Tsinθ=ω2L(1+sinθ) ............(i)
Applying Newton's second law in the vertical direction:
Tcosθ=mg ..........(ii)

Dividing (i) by (ii),
tanθ=ω2L(1+sinθ)g
or ω2=gtanθL(1+sinθ)
Putting the values, we get,
ω=4.4 rad/s

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon