If the gravitational field in space is given | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The relationship between gravitational field $E$ and potential $V$ is given by $E = -\frac{dV}{dr}$.Given $E = -\frac{K}{r^2}$,we have $-\frac{dV}

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(B) The relationship between gravitational field $E$ and potential $V$ is given by $E = -\frac{dV}{dr}$.Given $E = -\frac{K}{r^2}$,we have $-\frac{dV}{dr} = -\frac{K}{r^2}$,which implies $dV = \frac{K}{r^2} dr$.Integrating both sides from the reference point $(r_1 = 2\,cm, V_1 = 10\,J/kg)$ to the target point $(r_2 = 3\,cm, V_2 = V)$:$\int_{10}^{V} dV = \int_{2}^{3} \frac{K}{r^2} dr$.$V - 10 = K \left[ -\frac{1}{r} ight]_{2}^{3} = K \left( -\frac{1}{3} - (-\frac{1}{2}) ight) = K \left( \frac{1}{2} - \frac{1}{3} ight) = K \left( \frac{1}{6} ight)$.Substituting $K = 6\,J\cdot cm/kg$:$V - 10 = 6 	imes \frac{1}{6} = 1$.$V = 10 + 1 = 11\,J/kg$.

If the gravitational field in space is given as $E = -\frac{K}{r^2}$. Taking the reference point at $r = 2\,cm$ with gravitational potential $V = 10\,J/kg$. Find the gravitational potential at $r = 3\,cm$ in $SI$ units. (Given: $K = 6\,J\cdot cm/kg$)

Similar Questions

Two particles of mass $m$ and $9m$ are separated by a distance $r$. At a point on the line joining them,the gravitational field is zero. What is the gravitational potential at that point? ($G$ is the universal gravitational constant)

What is potential energy and gravitational potential energy? Write the dimensional formula of gravitational potential energy.

The gravitational potential energy is maximum at

The gravitational potential energy of a body of mass $m$ at a distance $r$ from the center of the Earth is $U$. Express the weight of the body at this point in terms of $U$.

Define gravitational potential energy. Obtain the formula for the gravitational potential energy of a body of mass $m$ at a distance $r$ $(r > R_E)$ from the centre of the Earth.

Vedclass Test Series

Exam Paper Generator

Online Exam Module