Consider the situation shown in the figure. A | vedclass

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

Question

(C) First,calculate the tension $T$ in the string connecting the masses $M$ and $2M$ over the movable pulley. The tension $T$ is given by the formula

Vedclass · Accepted Answer

$\frac{16}{3} M$

Vedclass · Answer

(C) First,calculate the tension $T$ in the string connecting the masses $M$ and $2M$ over the movable pulley. The tension $T$ is given by the formula for an Atwood machine: $T = \frac{2 M_1 M_2 g}{M_1 + M_2}$.Substituting $M_1 = M$ and $M_2 = 2M$,we get $T = \frac{2(M)(2M)g}{M + 2M} = \frac{4 M^2 g}{3M} = \frac{4}{3} Mg$.The movable pulley is supported by a string connected to the end of the rod. The upward force exerted on the rod by this string is equal to the tension in the string supporting the movable pulley,which is $2T = 2 	imes (\frac{4}{3} Mg) = \frac{8}{3} Mg$.Let $M'$ be the mass of the rod. The rod is in rotational equilibrium about hinge $A$. The torque due to the weight of the rod $(M'g)$ acting at its center of mass $(L/2)$ must balance the torque due to the upward force $(8/3 Mg)$ acting at the end of the rod $(L)$.Taking torque about $A$: $M'g 	imes \frac{L}{2} = \frac{8}{3} Mg 	imes L$.Simplifying,$\frac{M'}{2} = \frac{8}{3} M$,which gives $M' = \frac{16}{3} M$.

Consider the situation shown in the figure. $A$ uniform rod of length $L$ can rotate freely about the hinge $A$ in a vertical plane. Pulleys and string are light and frictionless. If the rod remains horizontal at rest when the system is released,then the mass of the rod is:

Similar Questions

In a physical balance working on the principle of moments,when $5\, mg$ weight is placed on the left pan,the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

$A$ car weighs $1800 \; kg$. The distance between its front and back axles is $1.8 \; m$. Its centre of gravity is $1.05 \; m$ behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.

$A$ metal rod of weight $W$ is supported by two parallel knife-edges $A$ and $B$. The rod is in equilibrium in a horizontal position. The distance between the two knife-edges is $r$. The centre of mass of the rod is at a distance $x$ from $A$. The normal reaction on $A$ is

State the principle of moments for a lever.

Vedclass Test Series

Exam Paper Generator

Online Exam Module