Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with side 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process is __________ J.

(Gravitational constant $G = 6.7 \times 10^{- 11} {N m}^{2} / {kg}^{2}$ ) [2026]

Question

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with side 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process is __________ J.

(Gravitational constant $G = 6.7 \times 10^{- 11} {N m}^{2} / {kg}^{2}$ ) [2026]

Smart Achievers · Accepted Answer

(2)

$Work done by external agent:$

$W_{ext} = Δ U$

$U_{i} = - \frac{G m_{1} m_{2}}{r_{i}} - \frac{G m_{2} m_{3}}{r_{i}} - \frac{G m_{1} m_{3}}{r_{i}} : r_{i} = 20 m$

$U_{f} = - \frac{G m_{1} m_{2}}{r_{f}} - \frac{G m_{2} m_{3}}{r_{f}} - \frac{G m_{1} m_{3}}{r_{f}} : r_{f} = 25 m$

$U_{i} = \frac{- 6.67 \times 10^{- 11}}{20} [200 \times 300 + 300 \times 400 + 200 \times 400]$

$= \frac{- 6.67 \times 10^{- 11}}{20} \times 26 \times 10^{4} = - 86.71 \times 10^{- 8} J$

$U_{f} = \frac{- 6.67 \times 10^{- 11}}{25} [200 \times 300 + 300 \times 400 + 200 \times 400]$

$= \frac{- 6.67 \times 10^{- 11}}{25} \times 26 \times 10^{4} = - 693.68 \times 10^{- 9}$

$= - 69.36 \times 10^{- 8} J$

$Δ U = U_{f} - U_{i} = 1.74 \times 10^{- 7} J$

Solution

1 $2.85 \times 10^{- 7}$

2 $1.74 \times 10^{- 7}$

3 $9.86 \times 10^{- 6}$

4 $4.77 \times 10^{- 7}$

Want Us to Email you About Special Offers & Updates?

Solution

1 2.85×10-7

2 1.74×10-7

3 9.86×10-6

4 4.77×10-7

Want Us to Email you About Special Offers & Updates?

1 $2.85 \times 10^{- 7}$

2 $1.74 \times 10^{- 7}$

3 $9.86 \times 10^{- 6}$

4 $4.77 \times 10^{- 7}$