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
Answers
Answer:
±5
Explanation:
It is correct ans. Because as we solve we get ±R/√2
And R=8cm
So8/√2=5.6 approx
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
