JEE Advanced 2014 · Paper 2 · Physics Q19

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PhysicsList match+3 / -1Question 19 of 60

A block of mass $m_1=1$ kg another mass $m_2=2$ kg, are placed together (see figure) on an inclined plane with angle of inclination $\theta$ . Various values of $\theta$ 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 $\mu=0.3$ . In List II expressions for the friction on block $m_2$ 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: $\tan(5.5^\circ)\approx0.1$ ; $\tan(11.5^\circ)\approx0.2$ ; $\tan(16.5^\circ)\approx0.3$ ]

An incline of angle θ (at the bottom right) with block m₁ placed above and touching block m₂ further down the slope, so m₁ pushes on m₂.

List I

P
$\theta=5^\circ$
Q
$\theta=10^\circ$
R
$\theta=15^\circ$
S
$\theta=20^\circ$

List II

1
$m_2g\sin\theta$
2
$(m_1+m_2)g\sin\theta$
3
$\mu m_2g\cos\theta$
4
$\mu(m_1+m_2)g\cos\theta$

P → 1; Q → 1; R → 1; S → 3

P → 2; Q → 2; R → 2; S → 3

P → 2; Q → 2; R → 2; S → 4

P → 2; Q → 2; R → 3; S → 3

Answer and worked solution

Official answer: D

When do the blocks stay at rest? $m_1$ (frictionless) presses on $m_2$ , so friction on $m_2$ must hold both. The most it can give is $\mu m_2g\cos\theta$ :
$(m_1+m_2)g\sin\theta\le\mu m_2g\cos\theta\iff\tan\theta\le\frac{0.3\times2}3=0.2\iff\theta\le11.5°.$

P (5°), Q (10°): at rest; static friction balances both blocks: $(m_1+m_2)g\sin\theta$ → 2.
R (15°), S (20°): the blocks slide, and kinetic friction is $\mu m_2g\cos\theta$ → 3.

(D) P → 2, Q → 2, R → 3, S → 3

Topics:Friction Free body diagrams

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JEE Advanced 2014 · Paper 2, Physics question 19