Answer:

Introduction:
When a member is subjected to like principal stresses, the greatest shear stress will occur on mutually perpendicular planes. The number of such planes depends upon the number of principal stresses present in the member.

Explanation:
There are three types of stresses that a member can be subjected to: tensile stress, compressive stress and shear stress. When a member is subjected to two principal stresses that are equal in magnitude but opposite in nature, the member experiences pure shear stress. In such a case, the greatest shear stress occurs on two mutually perpendicular planes.

Similarly, when a member is subjected to three principal stresses that are equal in magnitude but opposite in nature, the member experiences pure shear stress. In such a case, the greatest shear stress occurs on three mutually perpendicular planes.

However, when a member is subjected to two or three principal stresses that are not equal in magnitude, the member experiences combined stress. In such a case, the greatest shear stress still occurs on two mutually perpendicular planes.

Therefore, the answer to the question is option (1) 2 in number.

Conclusion:
In conclusion, when a member is subjected to like principal stresses, the greatest shear stress will occur on two mutually perpendicular planes. This is because the member experiences pure shear stress in such a case. When the member is subjected to two or three principal stresses that are not equal in magnitude, the member experiences combined stress and the greatest shear stress still occurs on two mutually perpendicular planes.