A small disc of radius 2 cm is cut from a disc of radius 6 cm. Distance between centres of disc is 3.2 cm. Find the distance of center of mass of remaining disc from center of original disc.

Question

A small disc of radius 2 cm is cut from a disc of radius 6 cm. Distance between centres of disc is 3.2 cm. Find the distance of center of mass of remaining disc from center of original disc. (A) 0.4 cm (B) 2.4 cm (C) 1.8 cm (D) 1.2 cm

Tardigrade Admin · Accepted Answer

Let radius of complete disc is a and that of small disc is

b

also let centre of mass now shifts to

O_{2}

at a distance

x_{2}

from original centre.
Solution

The position of new centre of mass is given by

X_{CM} = \frac{σ \cdot π b ^{2} \cdot x _{1}}{σ \cdot π a ^{2} - σ \cdot π b ^{2}}

Here,

a = 6 c m, b = 2 c m, x_{1} = 3.2 c m

Hence,

X_{CM} = \frac{- σ \times π ( 2 ^{2} \times 3.2 )}{σ \times π \times ( 6 ^{2} - σ \times π \times 2 ^{2} )}

= \frac{12.8 π}{32 π} = 0.4 c m

Q. A small disc of radius $2 c m$ is cut from a disc of radius $6 c m .$ Distance between centres of disc is $3.2 c m .$ Find the distance of center of mass of remaining disc from center of original disc.

$0.4 c m$

$2.4 c m$

$1.8 c m$

$1.2 c m$

Q. A small disc of radius 2cm is cut from a disc of radius 6cm. Distance between centres of disc is 3.2cm. Find the distance of center of mass of remaining disc from center of original disc.

0.4cm

2.4cm

1.8cm

1.2cm

Q. A small disc of radius $2 c m$ is cut from a disc of radius $6 c m .$ Distance between centres of disc is $3.2 c m .$ Find the distance of center of mass of remaining disc from center of original disc.

$0.4 c m$

$2.4 c m$

$1.8 c m$

$1.2 c m$