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 $II$ 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 $g$.
[Useful information : $\tan \left(5.5^{\circ}\right) \approx 0.1 ; \tan \left(11.5^{\circ}\right) \approx 0.2 ; \tan \left(16.5^{\circ} \approx 0.3\right)$ ]
List $I$
List $II$
$P.\quad$ $\theta=5^{\circ}$
$1.\quad$ $m _2 g \sin \theta$
$Q.\quad$ $\theta=10^{\circ}$
$2.\quad$ $\left(m_1+m_2\right) g \sin \theta$
$R.\quad$ $\theta=15^{\circ}$
$3.\quad$ $\mu m _2 g \cos \theta$
$S.\quad$ $\theta=20^{\circ}$
$4.\quad$ $\mu\left(m_1+m_2\right) g \cos \theta$
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 $II$ 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 $g$.
[Useful information : $\tan \left(5.5^{\circ}\right) \approx 0.1 ; \tan \left(11.5^{\circ}\right) \approx 0.2 ; \tan \left(16.5^{\circ} \approx 0.3\right)$ ]
| List $I$ | List $II$ |
| $P.\quad$ $\theta=5^{\circ}$ | $1.\quad$ $m _2 g \sin \theta$ |
| $Q.\quad$ $\theta=10^{\circ}$ | $2.\quad$ $\left(m_1+m_2\right) g \sin \theta$ |
| $R.\quad$ $\theta=15^{\circ}$ | $3.\quad$ $\mu m _2 g \cos \theta$ |
| $S.\quad$ $\theta=20^{\circ}$ | $4.\quad$ $\mu\left(m_1+m_2\right) g \cos \theta$ |
- [IIT 2014]
- 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
$P-2, Q-2, R-3,S-3$
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