Question

A toy car of mass 5 kg moves up a ramp under the influence of force F plotted against displacement. The maximum height attained is given by

A.${y_{\max }}$​=20 m
B. ${y_{\max }}$=15 m
C. ${y_{\max }}$​=11 m
D. ${y_{\max }}$​=5 m

Answer 1

In order to solve this type of question, we should observe the graph which gives the above force versus displacement. By using the work done by the body in terms of height and acceleration due to gravity.

Complete step by step answer:
Work done by the body is given by = $mgh$
Area under the graph is given by work done because work done =force ×displacement
From the right triangle,
Area of triangle =Work done
$\dfrac{1}{2} \times base \times height = mgh$
$\Rightarrow\dfrac{1}{2} \times 11 \times 100 = 5 \times 10 \times h$
$\Rightarrow h = \dfrac{{11 \times 50}}{{50}}\\\ \therefore h=11m$

Hence the correct option is C.

Additional information:
-Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position.
-Force can be defined as the push or pull of an object is considered a force. Push and pull come from the objects interacting with one another.

Note: Sometimes students may get confused with this type of question, whenever the graph is given with an area of rectangle and trapezium we need to use the formula of the same.