Question

A particle of 100 g mass is projected vertically up with a kinetic energy of 20 J. The maximum height reached by the particle is (\( g = 10 \) m/s\( ^2 \)) (neglecting air resistance).

• A. 5 m
• B. 10 m
• C. 15 m
• D. 20 m
• E. 25 m

Hint:

In problems involving vertical motion, energy conservation can simplify the calculation. Remember that the potential energy at the peak equals the initial kinetic energy.

Answer 1

The Correct Option is D

At the maximum height, all the kinetic energy is converted into potential energy. The gravitational potential energy at the maximum height is given by: \[ PE = mgh \] 
where: 
- \(m = 0.1 \, {kg}\) (mass), 
- \(g = 10 \, {m/s}^2\) (acceleration due to gravity), 
- \(h\) is the maximum height. 
The initial kinetic energy \(KE\) is 20 J. 
By conservation of energy: 
\[ KE = PE \quad \Rightarrow \quad 20 = 0.1 \times 10 \times h \] 
Solving for \(h\): \[ h = \frac{20}{1} = 20 \, {m} \] 
Hence, the correct answer is (D).