A projectile is projected with velocity k v_e | vedclass

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

Question

(C) Using the principle of conservation of mechanical energy between the surface of the Earth and the maximum height $h$ from the surface:Initial ener

Vedclass · Accepted Answer

$\frac{R}{1 - k^2}$

Vedclass · Answer

(C) Using the principle of conservation of mechanical energy between the surface of the Earth and the maximum height $h$ from the surface:Initial energy at the surface $= \frac{1}{2} m(k v_e)^2 - \frac{GMm}{R}$Final energy at maximum height $h = - \frac{GMm}{R+h}$Since $v_e = \sqrt{\frac{2GM}{R}}$,we have $v_e^2 = \frac{2GM}{R}$.Equating initial and final energy:$\frac{1}{2} m k^2 (\frac{2GM}{R}) - \frac{GMm}{R} = - \frac{GMm}{R+h}$$k^2 \frac{GMm}{R} - \frac{GMm}{R} = - \frac{GMm}{R+h}$$k^2 - 1 = - \frac{R}{R+h}$$1 - k^2 = \frac{R}{R+h}$$R+h = \frac{R}{1 - k^2}$Since the distance from the centre of the Earth is $r = R + h$,we get $r = \frac{R}{1 - k^2}$.

List-$I$	List-$II$
$(1)$ Heavy water	$(a)$ Bicarbonates of $Ca$ and $Mg$ in water
$(2)$ Temporary hard water	$(b)$ No foreign ions in water
$(3)$ Soft water	$(c)$ $D_2O$
$(4)$ Permanent hard water	$(d)$ Sulphates and chlorides of $Ca$ and $Mg$ in water

Similar Questions

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $\frac{g}{8}$,then the ratio of masses $m_2 : m_1$ is:

Which of the following substances acts as both an oxidizing agent and a reducing agent?

$A$ metal crystallises in a face-centred cubic $(FCC)$ structure. If the edge length of its unit cell is $a$,the closest approach between two atoms in the metallic crystal will be:

The cubic unit cell of a metal (molar mass $= 63.55 \ g \ mol^{-1}$) has an edge length of $362 \ pm$. Its density is $8.92 \ g \ cm^{-3}$. The type of unit cell is

Vedclass Test Series

Exam Paper Generator

Online Exam Module