
Figures I, II, III and IV depict the variation of force with time. In which situation, the impulse will be maximum?
(A) I and II
(B) III and I
(C) III and IV
(D) Only IV


Answer
475.2k+ views
Hint: In this question, we need to determine the graph (out of the given four graphs) which will give the maximum impulse. For this, we will use the relation between the impulse, force and time.
Complete step by step answer:
The product of the force and time for which the force has been applied is known as the impulse. Mathematically, $I = Ft$.
Here, the plots have been given for Force vs Time. So, to determine the impulse, we have to evaluate the area under each of the curves and compare the results for the maximum impulse.
(I)For the first plot, the curve given resembles a rectangle with 0.25 as the width and 1ms as the length. The area of the rectangle is given as the product of the length and the width of the rectangle. So, the impulse for the curve is given as:
$
\Rightarrow I = Ft \\
\Rightarrow I = 0.25 \times 1 \\
\Rightarrow I = 0.25 \\
$
(II) For the second plot, the curve given resembles a triangle which can be bifurcated into two right-angle triangles with 0.5 as the base and 0.3 as the height. The area of the right-angle triangle is given as half of the product of the base and the height of the triangle. So, the impulse for the curve is given as:
$
\Rightarrow I = Ft \\
\Rightarrow I = 2\left( {\dfrac{1}{2} \times b \times h} \right) \\
\Rightarrow I = 2\left( {\dfrac{1}{2} \times 0.5 \times 0.3} \right) \\
\Rightarrow I = 0.15 \\
$
(III) For the third plot, the curve given resembles a triangle which can be bifurcated into two right-angle triangles with 0.5 as the base and 1 as the height. The area of the right-angle triangle is given as half of the product of the base and the height of the triangle. So, the impulse for the curve is given as:
$
\Rightarrow I = Ft \\
\Rightarrow I = 2\left( {\dfrac{1}{2} \times b \times h} \right) \\
\Rightarrow I = 2\left( {\dfrac{1}{2} \times 0.5 \times 1} \right) \\
\Rightarrow I = 0.5 \\
$
(IV) For the fourth plot, the curve given resembles a right-angle triangle with 1 as the base and 1 as the height. The area of the right-angle triangle is given as half of the product of the base and the height of the triangle. So, the impulse for the curve is given as:
$
\Rightarrow I = Ft \\
\Rightarrow I= \left( {\dfrac{1}{2} \times b \times h} \right) \\
\Rightarrow I= \left( {\dfrac{1}{2} \times 1 \times 1} \right) \\
\Rightarrow I= 0.5 \\
$
Hence, we can say that the impulse is maximum for the curves (III) and (IV) with the equivalent value of 0.5.
Hence,option C is correct.
Note:The area under the curve can be calculated by bifurcating the plot into small parts and then adding all the parts to get the resultant area. Impulse is the integral of the force over the change in the time period.
Complete step by step answer:
The product of the force and time for which the force has been applied is known as the impulse. Mathematically, $I = Ft$.
Here, the plots have been given for Force vs Time. So, to determine the impulse, we have to evaluate the area under each of the curves and compare the results for the maximum impulse.
(I)For the first plot, the curve given resembles a rectangle with 0.25 as the width and 1ms as the length. The area of the rectangle is given as the product of the length and the width of the rectangle. So, the impulse for the curve is given as:
$
\Rightarrow I = Ft \\
\Rightarrow I = 0.25 \times 1 \\
\Rightarrow I = 0.25 \\
$
(II) For the second plot, the curve given resembles a triangle which can be bifurcated into two right-angle triangles with 0.5 as the base and 0.3 as the height. The area of the right-angle triangle is given as half of the product of the base and the height of the triangle. So, the impulse for the curve is given as:
$
\Rightarrow I = Ft \\
\Rightarrow I = 2\left( {\dfrac{1}{2} \times b \times h} \right) \\
\Rightarrow I = 2\left( {\dfrac{1}{2} \times 0.5 \times 0.3} \right) \\
\Rightarrow I = 0.15 \\
$
(III) For the third plot, the curve given resembles a triangle which can be bifurcated into two right-angle triangles with 0.5 as the base and 1 as the height. The area of the right-angle triangle is given as half of the product of the base and the height of the triangle. So, the impulse for the curve is given as:
$
\Rightarrow I = Ft \\
\Rightarrow I = 2\left( {\dfrac{1}{2} \times b \times h} \right) \\
\Rightarrow I = 2\left( {\dfrac{1}{2} \times 0.5 \times 1} \right) \\
\Rightarrow I = 0.5 \\
$
(IV) For the fourth plot, the curve given resembles a right-angle triangle with 1 as the base and 1 as the height. The area of the right-angle triangle is given as half of the product of the base and the height of the triangle. So, the impulse for the curve is given as:
$
\Rightarrow I = Ft \\
\Rightarrow I= \left( {\dfrac{1}{2} \times b \times h} \right) \\
\Rightarrow I= \left( {\dfrac{1}{2} \times 1 \times 1} \right) \\
\Rightarrow I= 0.5 \\
$
Hence, we can say that the impulse is maximum for the curves (III) and (IV) with the equivalent value of 0.5.
Hence,option C is correct.
Note:The area under the curve can be calculated by bifurcating the plot into small parts and then adding all the parts to get the resultant area. Impulse is the integral of the force over the change in the time period.
Recently Updated Pages
Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Statement I Reactivity of aluminium decreases when class 11 chemistry CBSE

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

How many valence electrons does nitrogen have class 11 chemistry CBSE
