The time taken by an object to slide down a 4 | 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 	het

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 $t_r = \sqrt{\frac{2s}{g(\sin 	heta - \mu \cos 	heta)}}$.Given $t_r = n t_s$,so $t_r^2 = n^2 t_s^2$.$\frac{2s}{g(\sin 	heta - \mu \cos 	heta)} = n^2 \frac{2s}{g \sin 	heta}$.$\sin 	heta - \mu \cos 	heta = \frac{\sin 	heta}{n^2}$.$\mu \cos 	heta = \sin 	heta \left( 1 - \frac{1}{n^2} ight)$.$\mu = 	an 	heta \left( 1 - \frac{1}{n^2} ight)$.Since $	heta = 45^{\circ}$,$	an 45^{\circ} = 1$,so $\mu = 1 - \frac{1}{n^2}$.

The time taken by an object to slide down a $45^{\circ}$ rough inclined plane is $n$ times the time it takes to slide down a perfectly smooth $45^{\circ}$ inclined plane. The coefficient of kinetic friction between the object and the inclined plane is:

Similar Questions

If an inclined plane is made slowly horizontal by reducing its inclination with the horizontal,the component of weight parallel to the plane of a block resting on the inclined plane:

$A$ block is lying on an inclined plane which makes $60^\circ$ with the horizontal. If the coefficient of friction between the block and the plane is $0.25$ and $g = 10\,m/s^2$,then the acceleration of the block when it moves along the plane will be ........ $m/s^2$.

$A$ body of mass $2\,kg$ slides down with an acceleration of $3\,m/s^2$ on a rough inclined plane having a slope of $30^o$. The external force required to take the same body up the plane with the same acceleration will be ........ $N$ $(g = 10\,m/s^2)$.

The ratio of acceleration of block $A$ placed on a smooth incline to block $B$ placed on a rough incline is $2:1$. The coefficient of kinetic friction between block $B$ and the incline is .........

$A$ block of mass $15 \, kg$ is resting on a rough inclined plane as shown in the figure. The block is tied by a horizontal string which has a tension of $50 \, N$. The minimum coefficient of friction between the surfaces of contact is $(g = 10 \, m/s^2)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module