Three identical spheres, each of mass 1 kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is

Question

Three identical spheres, each of mass 1 kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is (A) (P Q+P R+Q R/3) (B) (P Q+P R/3) (C) (P Q+Q R/3) (D) (P R+Q R/3)

Tardigrade Admin · Accepted Answer

X CM =((MP)(0)+(MQ)(P Q)+(MR)(P R)/MP+MQ+MR) =(1 × 0+1 × P Q+1 × P R/1+1+1)=(P Q+P R/3)

Q. Three identical spheres, each of mass $1 k g$ are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked $P, Q, R$ respectively, the distance of centre of mass of the system from $P$ is

$\frac{PQ + PR + QR}{3}$

$\frac{PQ + PR}{3}$

$\frac{PQ + QR}{3}$

$\frac{PR + QR}{3}$

$X_{CM} = \frac{( M _{P} ) ( 0 ) + ( M _{Q} ) ( PQ ) + ( M _{R} ) ( PR )}{M _{P} + M _{Q} + M _{R}}$
$= \frac{1 \times 0 + 1 \times PQ + 1 \times PR}{1 + 1 + 1} = \frac{PQ + PR}{3}$

Q. Three identical spheres, each of mass 1kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P,Q,R respectively, the distance of centre of mass of the system from P is

3PQ+PR+QR​

3PQ+PR​

3PQ+QR​

3PR+QR​