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Question:

A uniform disc is acted by two equal forces of magnitude F. One of them acts tangentially to the disc, while the other one is acting at the central point of the disc. The friction between the disc surface and the ground surface is nF. If r be the radius of the disc, then the value of n would be (in N):

1.2

3.2

0

2

Solution:

As evident from the question we shall formulate the equation for linear and angular acceleration separately.
Linear equation of motion : 2F − nF = ma.. (1)
where nF is friction and a is linear acceleration.
Angular equation of motion : τo = Iα
Moment of inertia of disc about point O I = 0.5mr²
(F + nF)r = 0.5mr²α
where α is angular acceleration.
Also we know a = rα
We get (F + nF) = 0.5ma (2)
From equation (1) - 2 x equation (1), we get
2nF = 0
⇒ n = 0
Hence, the value of n is 0.