A block of mass m 1 = 1 kg and another mass m 2 = 2 kg, are placed together (see figure) on an inclined plane with angle of inclination θ. Various values of θ are given in List I. The coefficient of friction between the block m 1 and the plane is always zero. The coefficient of static and dynamic friction between the block m 2 and the plane are equal to µ = 0.3. In List II expression for the friction on block m 2 given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option. The acceleration due to gravity is denoted by g.
List-I List-II
(P) θ = 5° ( 1) m 2 g sin θ
(Q) θ = 10° ( 2) (m 1 + m 2 ) g sin θ
(R) θ = 15° ( 3 ) µ m 2 g cos θ
(S) θ = 20° ( 4) µ (m 1 + m 2 ) g cos θ
Code:
Text Solution
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Sol. Block will not slip if
(m 1 + m 2 ) g sin θ ≤ μ m 2 g cos θ
3 sin θ ≤ 
cos θ
tan θ ≤ 
⇒ 
(P) θ = 5° friction is static f = (m 1 + m 2 ) g sin θ
(Q) θ = 10° friction is static f = (m 1 + m 2 ) g sin θ
(R) θ = 15° friction is kinetic f = μ m 2 g cos θ
(S) θ = 20° friction is kinetic f = μ m 2 g cos θ
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