Question

What is the work done to lift a body of mass 5 kg to a height of 50 m from the ground (in J)? (g=10 $m{s}^{-2}$)

• A. $250$
• B. $2.5\times {10}^{10}$
• C. $2.5\times {10}^3$
• D. $2.5\times {10}^{-4}$

Answer 1

The correct option is C

$2.5\times {10}^3$

The explanation for the correct answer

Step 1: Given Data

The mass$\left(m\right)$ of the body is$5kg$.

Initially, the body was on the ground.

The body is lifted to a height$\left(h\right)$ of$50m$.

Step 2: Calculation of work done

The value of work done will be equal to the change in potential energy of the body when the body is lifted from the ground to the height($50m$).

Mathematically$W=K_f-K_i$. Here$K_i=initialpotentialenergy,K_f=finalpotentialenergy$.

Potential energy =$mgh$ ($m=mass,g=accelerationduetogravity=10m{s}^{-2},h=height$)

initial potential energy (when the body is on the ground) will be$K_i=mgh$

Here$h=0$, so$K_i=5\times 10\times 0=0J$

Similarly, final potential energy ( when the body is at height$50m$) will be$K_f=mgh=5\times 10\times 50=2500J$

Now the work done will be$W=K_f-K_i$

$\Rightarrow W=2500-0=2500J$ =$2.5\times {10}^{3}J$

Hence, the correct answer is (C).