Verified Solution • 2025–26 Session moderate

QJEEM22Ph7f11: JEE Main 2022 Physics - Class 11 JEEM22Ph7f11 Solution: A body of mass is projected with velocity in vertically upward…

A body of mass m\mathrm{m} is projected with velocity λ ve\lambda \,v_{\mathrm{e}} in vertically upward direction from the surface of the earth into space. It is given that vev_{\mathrm{e}} is escape velocity and \lambda<1 . If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be :

(R : radius of earth)

Multiple Choice Options

  • A R1+λ2\frac{\mathrm{R}}{1+\lambda^{2}}
  • B R1−λ2\frac{R}{1-\lambda^{2}}
  • C R1−λ\frac{R}{1-\lambda}
  • D λ2R1−λ2\frac{\lambda^{2} \mathrm{R}}{1-\lambda^{2}}

Step-by-Step Verified Solution

Using energy conservation

−GMemRe+12m(λ2GMeRe)2=−GMemr- {{G{M_e}m} \over {{R_e}}} + {1 \over 2}m{\left( {\lambda \sqrt {{{2G{M_e}} \over {{R_e}}}} } \right)^2} = - {{G{M_e}m} \over r}

GMemr=GMemRe−GMemReλ2{{G{M_e}m} \over r} = {{G{M_e}m} \over {{R_e}}} - {{G{M_e}m} \over {{R_e}}}{\lambda ^2}

r=Re1−λ2r = {{{R_e}} \over {1 - {\lambda ^2}}}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring