Question

two blocks of masses M and 2m are at the height of h and h/2 respectively from the ground if U1 and U2 a potential energies of the two blocks respectively which of the following is correct
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Answer 1

Answer:

U1=U2

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Answer 2

Given,

Two blocks with masses,

1st block = m, and,

2nd block = 2m.

Height from the ground,

1st block = h, and,

2nd block = h/2.

Potential energies of 1st block = $U_1$, and 2nd block = $U_2$.

To find,

Relation between $U_1$ and $U_2$.

Solution,

We can solve this numerical problem following the process given below.

Firstly, let's know what potential energy means and how is it calculated. So the energy stored by a body by the virtue of its position relative to some other object or position is known as the potential energy. For example, a ball raised above the ground at some height possesses potential energy.

The potential energy stored in a body is given by,

$U=mgh$

Where m = mass of the body,

g = acceleration due to gravity,

h = height to which the body is raised above the ground.

So, for the given problem, the potential energy of the 1st block will be,

$U_1=mgh$

Similarly, for the 2nd block with mass (2m) and at height (h/2), potential energy,

$U_2=(2m)g(\frac{h}{2} )$

Simplifying,

$U_2=mgh$

So, from the above equations for $U_1$ and $U_2$, we see that the value for both is equal, that is,

$U_1=U_2=mgh$

⇒ $U_1=U_2$

Therefore, for the given system of blocks, the correct relation between the potential energies of both will be $U_1=U_2$.