Thin Spherical Shells

Q. A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1% with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

1. 0
2. 1
3. 1.08
4. 2.02

Q. A thin cylindrical tube closed at ends is subjected to internal pressure. A torque is also applied to the tube. The principal stresses $p_1$ and $p_2$ developed are $80.0$ units and $20.0$ units respectively. If the yield stress is $240$ units, then what is the factor of safety according to maximum shear stress theory?

1. $3.00$
2. $4.00$
3. $5.00$
4. $6.00$

Q. Consider the following statements in respect of a thick cylinder subjected to internal pressure:
1. The stress on an element on the outer wall is unidirectional.
2. The stresses on an element on the inner wall are principal stresses.
3. The constants of the Lame's equation are positive.
Which of these statements are correct?

1. $1$ and $2$
2. $1$ and $3$
3. $2$ and $3$
4. $1,2$ and $3$