Question

A rocket of mass $3\times {10}^{6}kg$ takes off from a launching pad and acquires a vertical velocity of $1km{s}^{-1}$ at an altitude of $25km$. The potential energy of the rocket is: [ Take $g=10m{s}^{-2}$]

• A. $7.5\times {10}^{11}J$
• B. $2.5\times {10}^{11}J$
• C. $7.5\times {10}^{10}J$
• D. $5.5\times {10}^{11}J$

Answer 1

The correct option is A

$7.5\times {10}^{11}J$

Step 1: Given

Mass, $m=3\times {10}^{6}kg$

Vertical velocity, $v=1km{s}^{-1}$

Acceleration due to gravity, $g=10m{s}^{-2}$

Height, $h=25km=25000m$

Potential energy, $P.E.=?$ ( To be calculated)

Step 2: Calculating the potential energy

$$\begin{gathered} PotentialEnergy(P.E.)=Mass\left(m\right)\times Accelerationduetogravity\left(g\right)\times Height\left(h\right) \\ \Rightarrow P.E.=m\times g\times h \\ \Rightarrow P.E.=3\times {10}^{6}kg\times 10m{s}^{-2}\times 25000m \\ \Rightarrow P.E.=7.5\times {10}^{11}J \end{gathered}$$

Therefore, the potential energy of the rocket is $7.5\times {10}^{11}J$

Hence, the correct answer is option (A) i.e., $7.5\times {10}^{11}J$.