Gravitational potential energy and gravitational potential
- Two bodies of mass m and 9m are placed at a distance R. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (G = gravitational constant) : Answer: 4. -16Gm/R Find the point where the net field is zero, then add the potentials of both masses there. Let the point be at distance x... 1
- A particle of mass 'm' is projected with a velocity v = kV_e (k < 1) from the surface of the earth. (V_e = escape velocity)The maximum height above the surface reached by the particle is : Answer: 4. Rk²/1-k² Key idea: conserve energy: 1/2mv²-dfracGMmR=-GMm/R+h , with V_e²=dfrac2GMR . 1/2m k²dfrac2GMR-dfracGMmR=-GMm/R+h⇒dfracGM... 1
- The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is : Answer: 3. 1/2mgR Work done = change in gravitational potential energy. W=-GMm/R+h+GMm/R . With h=R : W=GMm(1/R-dfrac12R)=GMm/2R . Using GM=... 1
- At what height from the surface of earth the gravitation potential and the value of g are -5.4×10^7\ J kg^-2 and 6.0\ ms^-2 respectively ? Take the radius of earth as 6400 km : Answer: 1. 2600 km Key idea: V=-GM/r and g=GM/r² , so r=|V|/g . r=dfrac5.4×10⁷6.0=9.0×10⁶ m =9000 km. Height h=r-R_E=9000-6400=2600 km. 1