Question

Calculate the potential energy of an object of mass 6 kg placed at a height of 12 m from the ground (g=10
m/s). How much will be the potential energy if the mass is doubled? ​

Answer 1

Given :

• Mass of an object = 6 kg
• Height = 12 m
• acceleration due to gravity (g) = 10 m/s²

To Find :

• Potential energy of given body and potential energy of the given body when it's mass is doubled

Solution :

The potential energy of a body is given by ,

$\\ \star \: {\boxed{\purple{\sf{PE = mgh}}}}$

$\\ \sf{where}\begin{cases} & \sf{m \: is \: mass \: of \: the \: body}\\ & \sf{g \: is \: acceleration \: due \: to \: gravity} \\ &\sf{h \:is \: height}\end{cases}$

Substituting the values we have ,

$\\ : \implies \sf \:PE = \: (6 \: kg) (10 \: m {s}^{ - 2} )(12 \: m )$

$\\ : \implies \sf \: PE =6 \times 10 \times 12 \: kg. {m}^{2} {s}^{ - 2}$

$\\ : \implies{\underline{\boxed{\pink{\sf{\: PE =720 \: J}}}}} \: \bigstar$

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Given mass = 6kg

Mass of the body , when it is doubled is = 6 × 2 = 12 kg

Now ,

$\\ \sf{we \: have}\begin{cases} & \sf{m \: = 12 \: kg}\\ & \sf{g \: = 10 \: m {s}^{ - 2} } \\ &\sf{h \: = 12 \: m}\end{cases}$

Substituting the values in the formula ,

$\\ : \implies \sf \: PE = (12 \: kg)(10 \: m{s}^{ - 2} )(10 \: m)$

$\\ : \implies \sf \: PE =12\times 10 \times 12 \: kg. {m}^{2} {s}^{ - 2}$

$\\ : \implies{\underline{\boxed{\pink{\sf{\: PE =1440 \: J}}}}} \: \bigstar$

Hence ,

• The original potential energy of the body = 720 J and the potential energy of the body when it's mass is doubled is 1440 J

Note :

$\\ \sf{\longmapsto J = Kg.m^2s^{-2}}$

Answer 2

Answer:

Explanation:

Given,

Mass of an object, m = 6 kg

Height, h = 12 m

acceleration due to gravity, g = 10 m/s

To Find,

(i) Potential energy and,

(ii) Potential energy if the mass is doubled.

Formula to be used,

P.E = mgh

Solution,

Solving (i), at first

Putting all the values, we get

P.E = mgh

⇒ P.E = 6 × 10 × 12

⇒ P.E = 720 J

Hence, the potential energy of an object is 720 J.

Now, potential energy if the mass is doubled.

Mass of an object, m = 6 kg  = 6 × 2 = 12 kg

And all will reamin same.

P.E = mgh

⇒ P.E = 12 × 10 × 12

⇒ P.E = 1440 J

Hence, the potential energy of an object is 1440 J.