Question:
A ball of mass 0.25 kg attached to the ends of a string of length 1.96 m is rotating in a horizontal circle. The string will break, if tension is more than 25 N. What is the maximum velocity with which the ball can be rotated?
A ball of mass 0.25 kg attached to the ends of a string of length 1.96 m is rotating in a horizontal circle. The string will break, if tension is more than 25 N. What is the maximum velocity with which the ball can be rotated?
Updated On: Jul 18, 2024
- 3 $ ms^{ - 1} $
- 5 $ ms^{ - 1} $
- 9 $ ms^{ - 1} $
- 14 $ ms^{ - 1} $
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
F = $ \frac{ mv^2 }{ r } $
or $ v^2 = \frac{ F r }{ m } $
$ \therefore v^2 = \frac{ 25 \times 1.96 }{ 0.25 } = 196 $
or $ v = \sqrt{ 196 } = 14 \, ms^{ - 1} $
or $ v^2 = \frac{ F r }{ m } $
$ \therefore v^2 = \frac{ 25 \times 1.96 }{ 0.25 } = 196 $
or $ v = \sqrt{ 196 } = 14 \, ms^{ - 1} $
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration