A rod of mass m and length l is hinged at one of its end A as shown in figure. A force F is applied at a distance x from A . The acceleration of the centre of mass (a) varies with x as -

Question

A rod of mass m and length l is hinged at one of its end A as shown in figure. A force F is applied at a distance x from A . The acceleration of the centre of mass (a) varies with x as - Question

(A)

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

The rod will rotate about point A with angular acceleration: α =(τ/I)=(F x/(m l2)3)=(3 F x/m l2) ∴ a =(l/2) α =(3/2)(F x/m l) or a propto x i.e., a text-x graph is a straight line passing through the origin.

Q. A rod of mass $m$ and length $l$ is hinged at one of its end $A$ as shown in figure. A force $F$ is applied at a distance $x$ from $A$ . The acceleration of the centre of mass $(a)$ varies with $x$ as -

The rod will rotate about point $A$ with angular acceleration:
$α = \frac{τ}{I} = \frac{F x}{\frac{m l ^{2}}{3}} = \frac{3 F x}{m l ^{2}}$
$∴ a = \frac{l}{2} α = \frac{3}{2} \frac{F x}{m l}$
or $a \propto x$
i.e., $a - x$ graph is a straight line passing through the origin.

Q. A rod of mass m and length l is hinged at one of its end A as shown in figure. A force F is applied at a distance x from A . The acceleration of the centre of mass (a) varies with x as -

The rod will rotate about point A with angular acceleration: α=Iτ​=3ml2​Fx​=ml23Fx​ ∴a=2l​α=23​mlFx​ or a∝x i.e., a-x graph is a straight line passing through the origin.

Q. A rod of mass $m$ and length $l$ is hinged at one of its end $A$ as shown in figure. A force $F$ is applied at a distance $x$ from $A$ . The acceleration of the centre of mass $(a)$ varies with $x$ as -

The rod will rotate about point $A$ with angular acceleration:
$α = \frac{τ}{I} = \frac{F x}{\frac{m l ^{2}}{3}} = \frac{3 F x}{m l ^{2}}$
$∴ a = \frac{l}{2} α = \frac{3}{2} \frac{F x}{m l}$
or $a \propto x$
i.e., $a - x$ graph is a straight line passing through the origin.