Question

A block of mass m₁ = 1 kg another mass m₂ = 2kg, 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 m₁ and the plane is always zero. The coefficient of static and dynamic friction between the block m₂ and the plane are equal to µ = 0.3. in List II expressions for the friction on the block m2 are 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.

[Useful information : tan(5.5°) ≈ 0.1; tan (11.5°) ≈ 0.2; tan(16.5°) ≈ 0.3]

	List I		List II
(P)	θ = 5°	(1)	m2g sinθ
(Q)	θ = 10°	(2)	(m1 + m2) g sinθ
(R)	θ = 15°	(3)	mm2 g cosθ
(S)	θ = 20°	(4)	µ(m1 + m2) g cosθ

Code: 

(A) (P)→(1), (Q)→(1), (R)→(1), (S)→(1) 

(B) (P)→(2), (Q)→(2), (R)→(2), (S)→(3) 

(C) (P)→(2), (Q)→(2), (R)→(2), (S)→(4) 

(D) (P)→(2), (Q)→(2), (R)→(3), (S)→(3)

Answer 1

Correct option is (D) (P)→(2), (Q)→(2), (R)→(3), (S)→(3)

Condition for not sliding,

f_max > (m₁ + m₂) g sin θ

µN > (m₁ + m₂) g sin θ

0.3 m₂ g cos θ ≥ 30 sin θ

6 ≥ 30 tan θ

1/5 ≥ tan θ

0.2 ≥ tan θ

∴ for P, Q

f = (m₁ + m₂) g sin θ

For R and S

F = f_max = µm₂ g sin θ

Answer 2

Correct answer is

(D) (P)→(2), (Q)→(2), (R)→(3), (S)→(3)