(B) The torque $\tau$ acting on the rod about the hinge is given by $\tau = F \times r$,where $r = 5L/6$ is the distance from the hinge.Given $F = Mg/

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(B) The torque $\tau$ acting on the rod about the hinge is given by $\tau = F \times r$,where $r = 5L/6$ is the distance from the hinge.Given $F = Mg/2$,the torque is $\tau = (Mg/2) \times (5L/6) = 5MgL/12$.The moment of inertia $I$ of a rod of mass $M$ and length $L$ about an axis passing through one of its ends is $I = ML^2/3$.Using the rotational analog of Newton's second law,$\tau = I\alpha$,where $\alpha$ is the angular acceleration:$5MgL/12 = (ML^2/3) \times \alpha$$\alpha = (5MgL/12) \times (3/ML^2)$$\alpha = 5g/4L$.

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

Difficult

$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane. One of its ends is hinged on a vertical axis. $A$ horizontal force $F = Mg/2$ is applied at a distance of $5L/6$ from the hinged end. What will be the angular acceleration of the rod?

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

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$A$ solid disc has a diameter of $0.5 \ m$ and a mass of $16 \ kg$. What torque must be applied to increase its angular velocity from $0$ to $120 \ rpm$ in $8 \ s$?

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$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane. One of its ends is hinged on a vertical axis. $A$ horizontal force $F = Mg/2$ is applied at a distance of $5L/6$ from the hinged end. What will be the angular acceleration of the rod?

Similar Questions

$A$ thin solid disk of $1 \ kg$ is rotating along its diameter axis at the speed of $1800 \ rpm$. By applying an external torque of $25 \pi \ Nm$ for $40 \ s$,the speed increases to $2100 \ rpm$. The diameter of the disk is . . . . . . $m$.

Write the Newton's second law for rotational motion about a fixed axis.

$A$ rigid body rotates about a fixed axis with variable angular velocity equal to $(\alpha - \beta t)$ at time $t,$ where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is

In the given figure,$r_1$ and $r_2$ are $10 \ cm$ and $20 \ cm$ respectively. If the moment of inertia of the wheel is $1500 \ kg \cdot m^2$,find the angular acceleration.

$A$ solid disc has a diameter of $0.5 \ m$ and a mass of $16 \ kg$. What torque must be applied to increase its angular velocity from $0$ to $120 \ rpm$ in $8 \ s$?

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