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  • Mass is at a distance '2a' from the centre of a ring of radius 'a' along the axis of the ring . Point

Mass m_0 is at a distance '2a' from the centre of a ring of radius 'a' along the axis of the ring . Point P is situated midway between the centre of the ring and m_0 on the axis of the ring. What should be the mass(M) of the ring such that the gravitational field at point P  is zero:

Option: 1

 (m_o)^{\frac{3}{2}}


Option: 2

(2m_o)^\frac{2}{3}


Option: 3

(2)^{\frac{3}{2}}m_o


Option: 4

(m_o)^{\frac{1}{2}}


Answers (1)

best_answer

 

Field due to point mass mo at P

E_{1}=\frac{Gm_{0}}{a^{2}}

Field due to ring at point p

E_{2}=\frac{GMa}{(a^{2}+a^{2})^{\frac{3}{2}}}

=\frac{GMa}{(2a^{2})^{\frac{3}{2}}}

If the net field at point p is zero these two fields should be equal.

E_{1}=E_{2}

\frac{Gmo}{a^{2}}=\frac{GMa}{(2a^{2})^{\frac{3}{2}}}

\frac{m_{0}}{a^{2}}=\frac{Ma}{(2)^{\frac{3}{2}}a^{3} }

M=(2)^{\frac{3}{2}}m_{0}

Posted by

rishi.raj

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