JEE Mains · Physics · STD 11 - 7. gravitation
If the gravitational field in the space is given as \(\left(-\frac{ K }{ r ^2}\right)\). Taking the reference point to be at \(r =2\,cm\) with gravitational potential \(V =10\,J / kg\). Find the gravitational potential at \(r =3\,cm\) in \(SI\) unit (Given, that \(K =6\,J cm / kg\) )
- A \(9\)
- B \(11\)
- C \(12\)
- D \(10\)
Answer & Solution
Correct Answer
(B) \(11\)
Step-by-step Solution
Detailed explanation
\(-\frac{ dV }{ dr }=-\frac{ k }{ r ^2} \Rightarrow \int \limits_{10}^{ V } dV =\int \limits_2^3 \frac{ k }{ r ^2} dr\) \(V -10= k \left[\frac{1}{2}-\frac{1}{3}\right]\) \(V -10=\frac{ k }{6} \Rightarrow V =11 \text { volts }\)
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