From a solid sphere of mass M and radius R, a spherical portion of radius R2 is removed, as shown in the figure. Taking gravitational potential V=0 at r=∞ , the potential at the centre of the cavity thus formed is : (G= gravitational constant)
−GMR
−2GM3R
−GM2R
−2GMR
A
−2GM3R
B
−GM2R
C
−GMR
D
−2GMR
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Solution
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Gravitational potential at any inside point is given as
V=−GM2R3(3R2−r2)....(i)
for r=R2V=−11GM8R
Subtracting potential due to cavity of mass Mc=M8 and Rc=R2
Gravitational potential at center is obtained by substituting r=0 in equation (i) =−3GMc2Rc
V=−11GM8R−(−3GMc2Rc)=−11GM8R+3GM82R2⇒V=−GMR
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Q1
From a solid sphere of mass M and radius R, a spherical portion of radius R2 is removed, as shown in the figure. Taking gravitational potential V=0 at r=∞ , the potential at the centre of the cavity thus formed is
(G= gravitational constant)
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Q2
From a solid sphere of mass M and radius R, a spherical portion of radius R2 is removed, as shown in the figure. Taking gravitational potential V=0 at r=∞ , the potential at the centre of the cavity thus formed is : (G= gravitational constant)
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Q3
From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure. Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is: (G = gravitational constant)