Physics · Mechanical Properties Of Solids · NEET
Yes. They are two names for the exact same quantity, symbol G. NCERT writes: 'the shear modulus of the material and is represented by G. It is also called the modulus of rigidity.' If a NEET question says modulus of rigidity, use the shear modulus formula G = (F/A)/(Delta x/L). Do not treat them as two different constants.
Longitudinal strain is Delta L / L (a change in LENGTH along the force). Shearing strain is Delta x / L, where Delta x is the sideways slide of the top face and L is the height. Because the slide is small, shearing strain also equals tan(theta), which is nearly equal to the angle theta itself. So shape changes, but the volume stays almost the same.
Shear modulus needs the material to resist a change in SHAPE. NCERT states: 'The Young's modulus and shear modulus are relevant only for solids since only solids have lengths and shapes.' Liquids and gases flow and cannot hold a fixed shape, so they have no shear modulus (for them a shear force just makes them flow). This is why transverse waves travel only in solids.
The SI unit is N/m^2 (pascal, Pa), the same as stress, because strain has no unit. Its dimensional formula is [M L^-1 T^-2]. Same unit as Young's modulus and bulk modulus - all three are moduli of elasticity, so all are measured in pascal.
It is generally easier to change a solid's shape (slide layers sideways) than to stretch it lengthwise. NCERT gives a handy NEET shortcut: 'For most materials G is about Y/3.' So if a problem gives Young's modulus but needs G, and no exact value is stated, G is roughly one-third of Y.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
G = shearing stress / shearing strain = (F/A) / (Delta x / L) = F x L / (A x Delta x). Since shearing strain equals the angle theta, it can also be written G = F / (A x theta).
For structural steel G is about 8.4 x 10^10 N/m^2 (aluminium about 2.5 x 10^10, copper about 4.4 x 10^10). Exact values are given in NCERT Table 8.2; in NEET problems use the value provided in the question.
The shear modulus. When a coil spring is pulled, the wire of the coil twists rather than stretches, so the deformation is set by G (modulus of rigidity), not Young's modulus. This is a common NEET assertion-reason point.
Rearrange G = (F/A)/(Delta x/L) to Delta x = (stress x L)/G = (F/A) x L / G. Example: for a lead slab (G = 5.6 x 10^9 N/m^2) with shear stress 1.8 x 10^6 N/m^2 and L = 0.5 m, Delta x = 1.6 x 10^-4 m = 0.16 mm.
No. A pure shear changes only the SHAPE of the solid; the volume stays essentially the same. Volume change is governed by the bulk modulus instead.
