Question

A stone of mass 100g is thrown upwards with a velocity 30m/s. What is the maximum
potential energy that can be gained by the stone?
(a) 45000J (b) 45J (c) 0J (d) 300J

Answer 1

☯ Potential energy ( U ) = 45J

• Maximum potential energy means , the body gained the potential energy at the maximum height .
• Mass of object = 100g = 0.1kg
• Velocity = 30m/s

____________________

♦ Maximum height :-

• v² - u² = - 2gH

☞ 0² - 30² = - 2 × (10) × (H)

☞ 0 - 900 = -20H

☞ H = 900/20

☞ Height = 45m

♦ Potential Energy :-

• U = mgh

☞ U = 0.1 × 10 × 45

☞ U = 1/10 × 10 × 45

☞ U = 1 × 45

☞ U = 45J

Answer 2

Gɪᴠᴇɴ :

• Mass of a stone 100 g.

$\longmapsto\:\bf{Mass\:(m)\:=\:100\:g\:=\:0.1\:kg}$

• The stone is thrown upwards with a velocity of 30 m/s.

$\longmapsto\:\bf{Velocity\:(v)\:=\:30\:m/s}$

Tᴏ Fɪɴᴅ :

• The maximum potential energy gained by the stone.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

We know that,

✯ When body reaches the highest point, it's entire kinetic energy gets converted into potential energy, which is maximum.

Thus,

↝ Kinetic energy of a body is,

$\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{Kinetic\:energy\:=\:\dfrac{1}{2}\:{m}\:{v^2}\:}}}}}}$

➛ $\bf{Kinetic\:energy\:=\:\dfrac{1}{2}\times{0.1}\times{(30)^2}\:}$

➛ $\bf{Kinetic\:energy\:=\:\dfrac{1}{2}\times{0.1}\times{900}\:}$

➛ $\bf{Kinetic\:energy\:=\:\dfrac{1}{2}\times{90}\:}$

➛ $\bf\blue{Kinetic\:energy\:=\:45\:Joules}$

Hence,

★ Here the maximum kinetic energy, i.e. 45 J is converted into potential energy (maximum).

➙ $\bf\pink{P.E_{(max^m)}\:=\:45\:Joules}$

[NOTE : Potential energy is maximum at highest point.]

$\Large\tt{Therefore,}$

The maximum potential energy gain by the stone is 45 J.