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A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point 25 m from the centre is V, the value of V is

Asked in JEE Main 27th Aug 2nd Shift 2021 · Potential of a sphere and a shell

• (1) +2G
• (2) -20G
• (3) -4G
• (4) -60G

Step-by-step solution

Why the other options are wrong

• (1) Has the right size for one term alone but the wrong sign; gravitational potential is never positive.
• (2) Reached by dividing the shell's mass by 5 rather than by its radius 50 m, a slip in the arithmetic of -(GM)/R.
• (4) Would need both masses divided by a distance far smaller than either 25 m or 50 m; no single substitution gives it.

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