Question

A uniform disc of radius 8 cm lies in the x – y plane, with its centre at origin. Its moment of inertia about z – axis is equal to its moment of inertia about the line 4y = 3x + 4c. where c is constant. Find the value of c

Answer 1

Answer:

±5

Explanation:

It is correct ans. Because as we solve we get ±R/√2

And R=8cm

So8/√2=5.6 approx

Answer 2

A uniform disc of radius 8 cm lies in the x – y plane, with its centre at origin. Its moment of inertia about z – axis is equal to its moment of inertia about the line 4y = 3x + 4c.

We have to find the value of c.

moment of inertia of disc about z - axis = moment of inertia of disc about an axis passing through its centre and perpendicular to its plane.

= 1/2 MR²

= 1/2 × M × (8cm)² ...(1)

moment of inertia of disc about the line 4y = 3x + 4c ⇒y = (3/4)x + c ⇒y = tan37° x + c

see diagram,

moment of inertia of disc about the line = moment of inertia of disc about diameter + mk² , where k is c cos37° [ perpendicular distance from origin to the line ]

= MR²/4 + Mk²

= M (8cm)²/4 + M × (c²cos²37°) ...(2)

from equations (1) and (2) we get,

(8cm)²/4 = c² cos²37°

⇒16 = c² × 16/25

⇒c = ±5 cm

Therefore the value of c is + 5 cm and -5cm