A composite rod made up of two rods AB and BC | vedclass

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

Question

(B) Let the length of each rod be $L$ and mass be $M$. The rods are joined at $B$. The center of mass of rod $AB$ is at a distance $L/2$ from $B$,and

Vedclass · Accepted Answer

It tilts down on the side of $AB$

Vedclass · Answer

(B) Let the length of each rod be $L$ and mass be $M$. The rods are joined at $B$. The center of mass of rod $AB$ is at a distance $L/2$ from $B$,and the center of mass of rod $BC$ is at a distance $L/2$ from $B$.When the rod is heated,the length of each rod increases according to the formula $\Delta L = L \alpha \Delta T$.Since $\alpha_{AB} > \alpha_{BC}$,the rod $AB$ expands more than the rod $BC$.Let the new lengths be $L_{AB}' = L(1 + \alpha_{AB} \Delta T)$ and $L_{BC}' = L(1 + \alpha_{BC} \Delta T)$.The new center of mass of rod $AB$ is at $L_{AB}'/2$ from $B$,and the new center of mass of rod $BC$ is at $L_{BC}'/2$ from $B$.Since $L_{AB}' > L_{BC}'$,the center of mass of rod $AB$ shifts further away from $B$ compared to the center of mass of rod $BC$.Because the rod is suspended at $B$,the torque due to the weight of rod $AB$ is $	au_{AB} = M g (L_{AB}'/2)$ and the torque due to the weight of rod $BC$ is $	au_{BC} = M g (L_{BC}'/2)$.Since $L_{AB}' > L_{BC}'$,the torque on the side of $AB$ is greater than the torque on the side of $BC$.Therefore,the rod tilts down on the side of $AB$.

Similar Questions

The density of a substance at $0^{\circ}C$ is $10 \, g/cm^3$ and at $100^{\circ}C$,its density is $9.7 \, g/cm^3$. The coefficient of linear expansion of the substance is:

$A$ cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap $x$ as shown. On heating the system:

When the temperature of a body increases from $T$ to $T+\Delta T$, its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body, then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

$A$ metal rod of silver at $0^{\circ}C$ is heated to $100^{\circ}C$. Its length increases by $0.19\, cm$. If the original length of the rod is $100\, cm$,the coefficient of cubical expansion of the silver rod is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module