A uniform rope lies on a horizontal table suc | vedclass

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

Question

(C) Let the total length of the rope be $L$ and its total mass be $M$. The mass per unit length is $\lambda = M/L$.The length of the hanging part is $

Vedclass · Accepted Answer

$0.33$

Vedclass · Answer

(C) Let the total length of the rope be $L$ and its total mass be $M$. The mass per unit length is $\lambda = M/L$.The length of the hanging part is $l = 0.25L = L/4$. The mass of the hanging part is $m = \lambda l = M/4$.The length of the part on the table is $L - l = 0.75L = 3L/4$. The mass of this part is $M' = \lambda(3L/4) = 3M/4$.The downward force causing the rope to slide is the weight of the hanging part: $F_g = mg = (M/4)g$.The limiting friction force opposing the motion is $f_s = \mu_s N = \mu_s M' g = \mu_s (3M/4)g$.At the point of sliding,the downward force equals the limiting friction force: $(M/4)g = \mu_s (3M/4)g$.Solving for $\mu_s$: $\mu_s = (M/4) / (3M/4) = 1/3 \approx 0.33$.

$A$ uniform rope lies on a horizontal table such that a part of it hangs over the edge. The rope begins to slide down when the length of the hanging part is $25\%$ of its entire length. The coefficient of friction between the rope and the table is

Similar Questions

$A$ body is sliding down an inclined plane (angle of inclination $45^{\circ}$). If the coefficient of friction is $0.5$ and $g = 9.8\, m/s^2$,then the acceleration of the body downwards in $m/s^2$ is

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:

$A$ block rests on a rough inclined plane making an angle of $30^o$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10 \, N$,the mass of the block (in $kg$) is (take $g = 10 \, m/s^2$)

$A$ block of mass $m$ slides down a plane inclined at an angle $\theta$. Which of the following will $NOT$ increase the energy lost by the block due to friction?

$A$ block of mass $2 \, kg$ rests on a rough inclined plane making an angle of $30^\circ$ with the horizontal. The coefficient of static friction between the block and the plane is $0.7$. The frictional force on the block is ....... $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module