Search any question & find its solution
Question:
Answered & Verified by Expert
A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth, maximum height attained by the body from the surface of the earth is
Options:
Solution:
1007 Upvotes
Verified Answer
The correct answer is:
$\frac{2 R}{3}$
Maximum height attained by a projectile
Velocity of body $=$ half the escape velocity
$v=\frac{v_e}{2}$
$\begin{aligned}
\text{or} \quad v=\frac{\sqrt{2 g R}}{2} \Rightarrow v^2=\frac{2 g R}{4} \\
\text{or} \quad v^2=\left(\frac{g R}{2}\right)
\end{aligned}$
Now, putting value of $v^2$ in Eq. (i), we get
$\begin{aligned}
h & =\frac{\frac{g R}{2} \cdot R}{2 g R-\frac{g R}{2}}=\frac{g R^2 / 2}{3 g R / 2} \\
\text { or } \quad h & =\frac{R}{3}
\end{aligned}$
Velocity of body $=$ half the escape velocity
$v=\frac{v_e}{2}$
$\begin{aligned}
\text{or} \quad v=\frac{\sqrt{2 g R}}{2} \Rightarrow v^2=\frac{2 g R}{4} \\
\text{or} \quad v^2=\left(\frac{g R}{2}\right)
\end{aligned}$
Now, putting value of $v^2$ in Eq. (i), we get
$\begin{aligned}
h & =\frac{\frac{g R}{2} \cdot R}{2 g R-\frac{g R}{2}}=\frac{g R^2 / 2}{3 g R / 2} \\
\text { or } \quad h & =\frac{R}{3}
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.