Question

A body of mass 5kg is raised vertically to a height of 10m by a force of $170N$. The velocity of the body at this height will be
$(A)15m/s$
$(B)37m/s$
$(C)9.8m/s$
$(D)22m/s$

Answer 1

In the question, the mass of the body, height, and force is given. With the assistance of those data, first, we will find the work done by the force and potential energy of the body. By using work done and potential energy values, we will calculate the Kinetic energy. After that, we are going to calculate the velocity of the body by using the kinetic energy formula.
Formula used:
The Kinetic energy $K.E = \dfrac{1}{2}m{v^2}$
Here, $K.E = W - P.E$, $P.E = mgh$ and $W = Fh$
Where,
$m =$ mass of the body,
$F =$ force, and
$v =$ velocity of the body.

Complete step-by-step solution:
Mass of body$m = 5kg$, Height of the body$h = 10m$, and Force$F = 170N$.
Work done by the force $W = Fh = 170 \times 10 = 1700J$.
Potential energy $P.E = mgh = 5 \times 10 \times 10 = 500J$ $\left( {\therefore g = 10N} \right)$
Kinetic Energy $K.E = W - P.E = 1700 - 500 = 1200J$
Therefore if the velocity of the body is$v$, we all know that
$K.E = \dfrac{1}{2}m{v^2}$
$\Rightarrow 1200 = \dfrac{1}{2} \times 5 \times {v^2}$
$\Rightarrow v = \sqrt {\dfrac{{2400}}{5}} = 21.9m/s$
Hence, the velocity of the body at this height is $22m/s$.

Note: Work done by a body is termed as the product of the force applied on a body and also the displacement produced within the body. Gravitational potential energy is the energy acquired by an object thanks to a shift in its position when it’s present in a gravitational field. In other words, it is stated that gravitational potential energy is an energy that’s linked to gravitational force. Kinetic energy is termed as the energy that is produced by an object because of its motion. When an object is ready to accelerate, there’s a precise must to apply certain forces. The application of force needs work, and after the work is completed, the energy gets transferred to the item making it move at a constant velocity.