Q

# Give answer! A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively:

• Option 1)

0.6 and 0.5

• Option 2)

0.5 and 0.6

• Option 3)

0.4 and 0.3

• Option 4)

0.6 and 0.6

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As we learnt in

Angle of Friction -

Angle $\theta$ is called angle of friction.

$tan\theta=\frac{F_{l}}{R}$

$tan\theta=\mu_{s}$

R = Reaction,      $\frac{F_{l}}{R}=\mu_{s}$

$F_{l}=$ Force of limiting friction

$\theta=tan^{-1}(\mu_{s})$

- wherein

$\mu_{s}=$ static friction coefficient

$\theta=$Angle made by resultant of limiting friction and R with the normal reaction.

$M_{s}=tan\: 30^{\circ}=\: \frac{1}{\sqrt{3}}=\: 0.6$

$S=ut+\frac{1}{2}at^{2},\ \: \: \: u=0,\ \: \: a=g(sin\theta-Mcos\theta)$

$4=\frac{1}{2}g (sin 30-M_kcos30)4^{2}$

$\Rightarrow 0.5\times 10\times \frac{1}{2}-M_k\times 10\times \frac{\sqrt{3}}{2}$

$\Rightarrow 5\sqrt{3}M_k=4.5\ \: \: \Rightarrow M_k=0.51$

Correct option is 1.

Option 1)

0.6 and 0.5

Correct

Option 2)

0.5 and 0.6

Incorrect

Option 3)

0.4 and 0.3

Incorrect

Option 4)

0.6 and 0.6

Incorrect

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