Question

a edge of a variable cube is increasing at the rate of 3cm/s .how fast is the volume of the cube increasing when the edge is 10 cm long ?

Answer 1

Answer:

Edge of the aluminium cube, L = 10 cm = 0.1 m

The mass attached to the cube, m = 100 kg

Shear modulus (η) of aluminium = 25 GPa = 25 × 109 Pa

Shear modulus, η = Shear stress / Shear strain = (F/A) / (L/ΔL)

Where,

F = Applied force = mg = 100 × 9.8 = 980 N

A = Area of one of the faces of the cube = 0.1 × 0.1 = 0.01 m2

ΔL = Vertical deflection of the cube

∴ ΔL = FL / Aη

= 980 × 0.1 / [ 10-2 × (25 × 109) ]

= 3.92 × 10–7 m

The vertical deflection of this face of the cube is 3.92 ×10–7 m.

Answer 2

Answer:

Explanation:

Please refer the below attachment.