Verified Solution • 2025–26 Session moderate

QAIPM-2011-Ph-1819: NEET 2011 Physics - Class 12 AIPM-2011-Ph-1819 Solution: A particle of mass M is situated at the centre of a spherical…

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre will be: GMa\frac{GM}{a} 2GMa\frac{2GM}{a} 3GMa\frac{3GM}{a} 4GMa\frac{4GM}{a}

Multiple Choice Options

  • A 2 N 0
  • B 3 N 0
  • C 9N02{{9{N_0}} \over 2} 2 9 N 0 _ _
  • D 5N02{{5{N_0}} \over 2} 2 5 N 0 _ _

Step-by-Step Verified Solution

Initially P = 4N 0 Q = N 0 Half life T P = 1 min. T Q = 2 min. Let after time t number of nuclei of P and Q are equal, that is N P = N Q _ 4 N 0 ( 1 2 ) t / 1 = N 0 ( 1 2 ) t / 2 _ 2 t / 1 = 4.2 t / 2 _ t = 4 min After 4 minutes, both P and Q have equal number of nuclei. _ Number of nuclei of R = ( 4 N 0 _ N 0 4 ) + ( N 0 _ N 0 4 ) = 9 N 0 2

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