Question

A uniform metal of radius r is taken and out of it a disc of diameter r/2 is cut off from the end ..The center of mass is

Answer 1

Answer:

Let mass of uniform metal disc of radius R is M.

so, mass of disc of diameter R/2 is M/πR² × π(R/4)² = M/16

now, Let's assume that centre of big disc is located at origin.

so, centre of small disc lies on axis at x = 3R/4

now use formula,

where M is mass of big uniform disc , m is mass of small uniform disc , X is the centre of big and x is the centre of small disc.

here, X = 0, x = 3R/4 and m = M/16

now, C.M = (M × 0 - M/16 × 3R/4)/(M - M/16)

CM = (-3R/4 × 16)/(15/16)

CM = -R/20

similarly you can use formula  to get y coordinate of centre of mass of remaining part.

but Y = 0, and y = 0, so, y coordinate of CM = 0

hence, centre of mass of remaining part is (-R/20, 0)

Explanation:

Answer 2

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