Three identical spheres, each of mass 1 kg are kept as shown in figure below, 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 below, 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)  (PQ+PR+QR/3)  (B)  (PQ+PR/3)  (C)  (PQ+QR/3)  (D)  (PR+QR/3)

Tardigrade Admin · Accepted Answer

r1=0,r2=PQ,r3=PR Distance of centre of mass from P is r=(r1+r2+r3/3) =(0+PQ+PR/3) =(PQ+PR/3)

Q. Three identical spheres, each of mass $1 k g$ are kept as shown in figure below, 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:

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

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

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

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

$\frac{PQ + QR + PR}{6}$

$r_{1} = 0, r_{2} = PQ, r_{3} = PR$
Distance of centre of mass from P is
$r = \frac{r _{1} + r _{2} + r _{3}}{3}$
$= \frac{0 + PQ + PR}{3}$
$= \frac{PQ + PR}{3}$

Q. Three identical spheres, each of mass 1kg are kept as shown in figure below, 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​

6PQ+QR+PR​

r1​=0,r2​=PQ,r3​=PR Distance of centre of mass from P is r=3r1​+r2​+r3​​ =30+PQ+PR​ =3PQ+PR​