A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

Question

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is (A)  (R /3) (B)  (R /2) (C)  (R /4) (D)  (R /5)

Tardigrade Admin · Accepted Answer

Total energy = K.E. + P.E. = (1/2) m ( (1/2) √(2GM/R))2 + (- (GMm/R)) = (GMm/4R) - (GMm/R) = - (3GMm/4R) Final energy when body comes to rest at heigh r = -(GMm/R) ∴ (-3GMm/4R) = (GMm/r) i.e. r = (4R/3) Max.height = r - R = (4/3) R - R = (R/3)

Q. A body is projected vertically upwards from the surface of a planet of radius $R$ with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

$\frac{R}{3}$

$\frac{R}{2}$

$\frac{R}{4}$

$\frac{R}{5}$

Q. A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

3R​

2R​

4R​

5R​

Total energy = K.E. + P.E. = 21​m(21​R2GM​​)2+(−RGMm​) = 4RGMm​−RGMm​=−4R3GMm​ Final energy when body comes to rest at heigh r=−RGMm​ ∴4R−3GMm​=rGMm​ i.e. r=34R​ Max.height = r - R = 34​ R - R = 3R​

Q. A body is projected vertically upwards from the surface of a planet of radius $R$ with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

$\frac{R}{3}$

$\frac{R}{2}$

$\frac{R}{4}$

$\frac{R}{5}$