Question

The potential energy of a body of mass 0.5 kg
increases by 100 J when it is taken to the top of
a tower from the ground. If force of gravity on
1 kg is 10 N, what is the height of the tower ?​

Answer 1

Answer ➪

• Mass of body M = 0.5kg

• Potential energy P.E = 100J

• Force of gravity on 1 kg is 10 N

→ F = mg

→ 10 = 1 × g

⇒ g = 10m/s²

change in Potential energy

= mg( h1 - h2 )

= mg( h - 0 )

= mgh

Height ⇒

100 = mgh

h    = 100 / (0.5 × 10)

​ h    = 20m

∴ The height of the tower is 20 m

Answer 2

Required solution -

${\large{\bold{\rm{\underline{Correct \; question}}}}}$

✠ The potential energy of a body of mass 0.5 kg increases by 100 J when it is taken to the top of a tower from the ground. If force of gravity on 1 kg is 10 N, what is the height of the tower ?

${\large{\bold{\rm{\underline{Given \; that}}}}}$

⇢ Mass of body = 0.5 kg

⇢ Potential energy of body increases by 100 Joules when it is taken to the top of a tower from the ground.

⇢ Force of gravity on 1 kg is 10 N.

${\large{\bold{\rm{\underline{To \; find}}}}}$

⇢ The height of the tower.

${\large{\bold{\rm{\underline{Solution}}}}}$

⇢ The height of the tower = 20 metres

${\large{\bold{\rm{\underline{Using \; concepts}}}}}$

↠ Formula to find force.

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

↠ F = mg

${\large{\bold{\rm{\underline{Where,}}}}}$

★ F denotes force

★ m denotes mass

★ g denotes acceleration due to gravity

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Let us solve this question, firstly using formula to find force let us find value of G according to the question.!

➙ F = mg

➙ 10 = 1 × g

➙ g = 10 m/s²

~ Let's see about change in potential energy..! (According to the question)

➙ mg(h1-h2)

➙ mg(h1-0)

➙ mgh

~ Let us find height of tower now..!

➙ 100 = mgh

➙ 100 = (0.5)(10)(h)

➙ 100 = 0.5 × 10 × h

➙ 100 = 5 × h

➙ 100/5 = h

➙ 20 = h

➙ h = 20 metres

${\frak{20 \: m \: is \: the \: tower's \: height}}$

${\large{\bold{\rm{\underline{Additional \; knowledge}}}}}$

♛ Energy = Capacity of doing work by a body is called it's energy. Energy is a scaler quantity & it's SI unit is ${\red{\bf{joule}}}$ Energy developed in a body due to work done on it is called mechanical energy. Mechanical energy is of two types –

• Potential energy
• Kinetic energy

➜ Potential energy = The capacity of doing work developed in a body due to it's position or configuration is known as potential energy like, ⑴ energy of stretched or compressed string ⑵ energy of spring in a watch ⑶ energy of water collected at a height.

PE of a body is the gravitational field of earth is ${\red{\bf{mgh}}}$

[Where, m denotes mass , g denotes acceleration due to gravity and h denotes height of the body from the surface of the earth].

➜ Kinetic energy = Energy posses by a body due to it's motion is called kinetic energy of the body. If a body of mass is moving with speed then kinetic energy of body is ${\red{\bf{\dfrac{1}{2}mv^{2}}}}$

[Where, m denotes mass and v denotes speed].

Rєlαtíσn вєtwєєn mσmєntum αnd kínєtíc єnєrgч –

${\red{\bf{K.E \: = \: \dfrac{p^{2}}{2m}}}}$

[Where, p = momentum = mv].