Question

A block of mass $m_1=1kg$ another mass $m_2=2kg$ are placed together (see figure) on an inclined plane with angle of inclination $\theta$ an inclined plane with angle of inclination $\theta$ 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 the 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 deoted by $g$.
[Useful information $\tan (5.5^{\circ })\approx 0.1;\tan (11.5^{\circ })\approx 0.2;\tan (16.5^{\circ })\approx 0.3$]

List I		List II
P	$\theta =5^{\circ }$	1	$m_{2}g\sin \theta$
Q	$\theta =10^{\circ }$	2	$(m_1+m_2)g\sin \theta$
R	$\theta =15^{\circ }$	3	$\mu m_{2}g\cos \theta$
S	$\theta =20^{\circ }$	4	$\mu (m_1+m_2)g\cos \theta$

• A. P-(1), Q-(1), R-(1), S-(3)
• 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

Answer: (D)

Condition for not sliding,
$f_{\max }>\left(m_1+m_2\right)g\sin \theta$
$\mu N>\left(m_1+m_2\right)g\sin \theta$
$0.3m_{2}g\cos \theta \ge 30\sin \theta$
$6\ge 30\tan \theta$
$1/5\ge \tan \theta$
$0.2\ge \tan \theta$
$\therefore$ for $P,Q$
$f=\left(m_1+m_2\right)g\sin \theta$
For $R$ and $S$
$F=f_{max}=\mu m_{2}g\sin \theta$