(B) The torque $\tau$ about the hinged end is given by $\tau = F \times r$,where $r = \frac{5L}{6}$.$\tau = \left( \frac{Mg}{2} \right) \times \left(

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(B) The torque $\tau$ about the hinged end is given by $\tau = F \times r$,where $r = \frac{5L}{6}$.$\tau = \left( \frac{Mg}{2} \right) \times \left( \frac{5L}{6} \right) = \frac{5MgL}{12}$.The moment of inertia $I$ of a rod about an axis passing through one end is $I = \frac{ML^2}{3}$.Using the relation $\tau = I \alpha$,where $\alpha$ is the angular acceleration:$\alpha = \frac{\tau}{I} = \frac{5MgL}{12} \times \frac{3}{ML^2}$.$\alpha = \frac{5g}{4L}$.

Class 11 Physics System of Particles and Rotational Motion Relation between Torque and Angular acceleration and it's Application

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$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane with one end hinged about a vertical axis. $A$ horizontal force of $F = \frac{Mg}{2}$ is applied at a distance $\frac{5L}{6}$ from the hinged end. The angular acceleration of the rod will be:

A
$\frac{4g}{5L}$
B
$\frac{5g}{4L}$
C
$\frac{3g}{4L}$
D
$\frac{4g}{3L}$

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

Consider a body shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = MV$ (where $V$ is the linear velocity of a ball) is imparted to the body at one of its ends,what would be its angular velocity?

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In the given figure,about which axis will the angular acceleration be greater if a force is applied at the midpoint of the triangular frame?

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$A$ constant torque acting on a wheel changes its angular momentum from $A_0$ to $4A_0$ in $4 \ s$. The magnitude of the torque is:

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$A$ disc of radius $0.4 \,m$ and mass $1 \,kg$ rotates about an axis passing through its center and perpendicular to its plane. The angular acceleration is $10 \,rad \,s^{-2}$. The tangential force applied to the rim of the disc is (in $\,N$)

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$A$ rope is wound around a hollow cylinder of mass $3\, kg$ and radius $40\, cm.$ What is the angular acceleration (in $rad/s^2$) of the cylinder if the rope is pulled with a force of $30\, N$?

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$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane with one end hinged about a vertical axis. $A$ horizontal force of $F = \frac{Mg}{2}$ is applied at a distance $\frac{5L}{6}$ from the hinged end. The angular acceleration of the rod will be:

Similar Questions

Consider a body shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = MV$ (where $V$ is the linear velocity of a ball) is imparted to the body at one of its ends,what would be its angular velocity?

In the given figure,about which axis will the angular acceleration be greater if a force is applied at the midpoint of the triangular frame?

$A$ constant torque acting on a wheel changes its angular momentum from $A_0$ to $4A_0$ in $4 \ s$. The magnitude of the torque is:

$A$ disc of radius $0.4 \,m$ and mass $1 \,kg$ rotates about an axis passing through its center and perpendicular to its plane. The angular acceleration is $10 \,rad \,s^{-2}$. The tangential force applied to the rim of the disc is (in $\,N$)

$A$ rope is wound around a hollow cylinder of mass $3\, kg$ and radius $40\, cm.$ What is the angular acceleration (in $rad/s^2$) of the cylinder if the rope is pulled with a force of $30\, N$?

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