Questions
A body of mass 5 X 10-3 kg is launched upon a rough inclined plane making an angle of 30° with the horizontal. Obtain the coefficient of friction between the body and the plane, if the time of ascent is half of the time of descent.
detailed solution
Correct option is A
According to question, the situation can be shown asCase 1 For body projected up the plane, v=0Using third equation of motion, v2=u2-2a1s⇒ 0=u2-2a1s∴ u=2a1sAlso v=u-a1t1⇒ 0=u-a1t1⇒ t1=u/a1∴ t1=2a1sa1=2sa1 …(i) As, ma1=μR+mgsinθ∴ Retardation, a1=μR+mgsin30°mAlso, R=mgcos30°⇒ a1=μmgcos30°+mgsin30°m=μg32+g2 …(ii)Case 2 For body coming down the plane,s=ut+12a2t22As u = 0⇒ t2=2s/a2 …(iii)Downward acceleration,a2=mgsin30°-μRm=mgsin30°-μmgcos30°m=g2-μg32 …(iv)Given, t1=t2/2Substituting values of t1 and t2 from Eqs. (i) and (iii), we get2sa1=122sa2Now, squaring both sides, we geta1=4a2 …(v)Substituting values of a1 and a2 from Eqs. (ii) and (iv) in Eq. (v), we getμg32+g2=4g2-μg32Solving μ, we getμ=35=1.7325⇒ μ=0.346Talk to our academic expert!
Similar Questions
The minimum force required to move a body up an inclined plane is three times the minimum force required to prevent it from sliding down the plane. If coefficient of friction between the body and inclined plane is , the angle of inclination of the plane with horizontal is
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