An object takes n times as much time to slide | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For a smooth inclined plane, the acceleration is $a_s = g \sin 	heta$. The time taken to cover distance $s$ is $t_s = \sqrt{\frac{2s}{g \sin 	he

Vedclass · Accepted Answer

$\left(1-\frac{1}{n^2}\right)$

Vedclass · Answer

(A) For a smooth inclined plane, the acceleration is $a_s = g \sin 	heta$. The time taken to cover distance $s$ is $t_s = \sqrt{\frac{2s}{g \sin 	heta}}$.For a rough inclined plane, the acceleration is $a_r = g(\sin 	heta - \mu \cos 	heta)$. The time taken is $t_r = \sqrt{\frac{2s}{g(\sin 	heta - \mu \cos 	heta)}} = n t_s$.Squaring both sides: $\frac{2s}{g(\sin 	heta - \mu \cos 	heta)} = n^2 \frac{2s}{g \sin 	heta}$.This simplifies to $\sin 	heta = n^2(\sin 	heta - \mu \cos 	heta)$, which gives $\mu \cos 	heta = \sin 	heta (1 - \frac{1}{n^2})$.Thus, $\mu = 	an 	heta (1 - \frac{1}{n^2})$.Given $	heta = 45^{\circ}$, $	an 45^{\circ} = 1$, so $\mu = 1 - \frac{1}{n^2}$.

An object takes $n$ times as much time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by:

Similar Questions

The upper half of an inclined plane with inclination $\phi$ is perfectly smooth,while the lower half is rough. $A$ body starting from rest at the top will again come to rest at the bottom,if the coefficient of friction for the lower half is given by-

$A$ small mass slides down an inclined plane of angle $\theta$ with the horizontal. The coefficient of friction is $\mu = \mu_0 x$,where $x$ is the distance through which the mass slides down and $\mu_0$ is a constant. Then,the distance covered by the mass before it stops is:

$A$ body is made to move up along an inclined plane of inclination $30^{\circ}$ and the coefficient of friction is $0.5$. Then its retardation is ($g$ = acceleration due to gravity).

$A$ block of mass $m$ is pressed against a vertical wall and is in equilibrium. An external upward force of $\frac{mg}{2}$ is applied to the block. The minimum coefficient of friction $\mu$ required is:

$A$ box is lying on an inclined plane. What is the coefficient of static friction if the box starts sliding when the angle of inclination is $60^\circ$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module