Question

A book of mass $0.5kg$ is lifted vertically upward by using energy of $1J$. The vertical distance through which book is raised:

• A. $40cm$
• B. $100cm$
• C. $50cm$
• D. $20cm$

Answer 1

The correct option is D

$20cm$

Step 1: Given

Vertical distance,$h=?$

Mass of book, $m=0.5kg$

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

Potential energy, $P.E.=1J$

Step 2: Mathematical expression for potential energy:

$$\begin{gathered} PotentialEnergy=mass\times accelerationduetogravity\times height \\ \therefore P.E.=m\times g\times h \end{gathered}$$

Step 3: By putting the values in the above expression, we get

$$\begin{gathered} P.E.=m\times g\times h \\ \Rightarrow 1J=0.5kg\times 10m{s}^{-2}\times h \\ \Rightarrow h=\frac{1J}{0.5kg\times 10m{s}^{-2}}=0.2m \\ \Rightarrow h=0.2\times 100cm=20cm \end{gathered}$$

Therefore, the vertical distance through which book is raised is $20cm$.

Hence, the correct answer is option (D) i.e. $20cm$.