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Question: Three particles each of mass 100 gm are brought from a very large distance to the vertices of an equ...

Three particles each of mass 100 gm are brought from a very large distance to the vertices of an equilateral triangle whose side is 20 cm in length. The work done will be

A

0.33×10−110.33 \times 10 ^ { - 11 } Joule

B

−0.33×10−11- 0.33 \times 10 ^ { - 11 } Joule

C

1.00×10−111.00 \times 10 ^ { - 11 } Joule

D

Answer

Explanation

Solution

Potential energy of three particles system

U=−Gm1m2r12−Gm2m3r23−Gm1m3r13U = - \frac { G m _ { 1 } m _ { 2 } } { r _ { 12 } } - \frac { G m _ { 2 } m _ { 3 } } { r _ { 23 } } - \frac { G m _ { 1 } m _ { 3 } } { r _ { 13 } }

Given m1=m2=m3=100gmm _ { 1 } = m _ { 2 } = m _ { 3 } = 100 \mathrm { gm }

and r12=r23=r13=2 cmr _ { 12 } = r _ { 23 } = r _ { 13 } = 2 \mathrm {~cm}

∴ U=3[−6.67×10−11×(10−1)×(10−1)20×10−2]U = 3 \left[ \frac { - 6.67 \times 10 ^ { - 11 } \times \left( 10 ^ { - 1 } \right) \times \left( 10 ^ { - 1 } \right) } { 20 \times 10 ^ { - 2 } } \right].