Shear Modulus

Q. The strain energy stored in a body of volume $V$ due to shear strain $\varphi$ is (shear modulus is $G$)

1. $\frac{{\varphi }^{2}V}{2G}$
2. $\frac{G\varphi V^2}{2}$
3. $\frac{\varphi V}{2G}$
4. $\frac{1}{2}G{\varphi }^{2}V$

Q.

The ratio of lengths of two rods A and B of same material is 1 : 2 and the ratio of their radii is 2 : 1, then the ratio of modulus of rigidity of A and B will be

1. 4 : 1

2. 16 : 1

3. 8 : 1

4. 1 : 1

Q.

Modulus of rigidity of a liquid

1. Non zero constant

2. Infinite

3. Nearly Zero

4. Can not be predicted

Q. Two rods A and B of the same material and length have their radii $r_1$ and $r_2$ respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end, the ratio of the angle of twist at the end of A and the angle of twist at the end of B is

1. $\frac{r_2^4}{r_1^4}$
2. $\frac{r_1^4}{r_2^4}$
3. $\frac{r_2^2}{r_1^2}$
4. $\frac{r_1^2}{r_2^2}$

Q. One of the square faces of a metal slab of side $50\text{cm}$ and thickness $20\text{cm}$ is rigidly fixed on a horizontal surface. If a tangential force of $30\text{N}$ is applied to the top face, then the displacement (in $\text{m}$) of the top face is :
[The shear modulus of the material is $4\times {10}^{10}{\text{N/m}}^2$]

1. $4\times {10}^{-12}$
2. $4\times {10}^{-10}$
3. $6\times {10}^{-10}$
4. $8\times {10}^{-10}$