A horizontal heavy uniform bar of weight W is supported at its ends by two men. At instant, on

English

Gujarati

Hindi

6.System of Particles and Rotational Motion

hard

A horizontal heavy uniform bar of weight $W$ is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to

A

$W$

B

$\frac{W}{2}$

C

$\frac{{3W}}{4}$

D

$\frac{W}{4}$

Solution

Let the mass of the rod is $M$

Weight ($W$) = $Mg$

Initially for the equilibrium $F + F = Mg$

$F = Mg/2$

When one man withdraws, the torque on the rod

$\tau = I\alpha = Mg\frac{l}{2}$

$\frac{{M{l^2}}}{3}\alpha = Mg\,\frac{l}{2}$ [As $I = Ml^2/ 3$]

Angular acceleration $\alpha = \frac{3}{2}\frac{g}{l}$and linear acceleration $a = \frac{l}{2}\alpha = \frac{{3g}}{4}$

Now if the new normal force at $A$ is $F'$ then $Mg – F' = Ma$

$F' = Mg – Ma = Mg – \frac{{3Mg}}{4}$$ = \frac{{Mg}}{4}$$ = \frac{W}{4}$.

Standard 11

Physics

Share

Similar Questions

$A\, 5\, m$ long pole of $3\, kg$ mass is placed against a smooth vertical well as shown in the figure. Under equilibrium condition, if the pole makes an angle of $37^o$ with the horizontal, the frictional force between the pole and horizontal surface is

hard

$A$ uniform ladder of length $5m$ is placed against the wall as shown in the figure. If coefficient of friction $\mu$ is the same for both the walls, what is the minimum value of $\mu$ for it not to slip?

normal

Two light vertical springs with equal natural lengths and spring constants $k_1$ and $k_2$ are separated by a distance $l$. Their upper ends are fixed to the ceiling and their lower ends to the ends $A$ and $B$ of a light horizontal rod $AB$. $A$ vertical downwards force $F$ is applied at point $C$ on the rod. $AB$ will remain horizontal in equilibrium if the distance $AC$ is

hard

$A$ body weighs $6$ gms when placed in one pan and $24$ gms when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is ……. $gm$.

hard

Write the conditions for equilibrium of a rigid body.

hard