A force acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant = 1 N then will be [2025]

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Solution

Q.
A force $F = α + β x^{2}$ acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant $α$ = 1 N then $β$ will be [2025]

1 $15 N / m^{2}$

2 $10 N / m^{2}$

3 $12 N / m^{2}$

4 $8 N / m^{2}$

Ans.
(3)

$F = α + β x^{2}$

Work done $\int d W = \int F \cdot d x$

$\Rightarrow △ W = \int F \cdot d x = \int (α + β x^{2}) d x$

$\Rightarrow △ W =$ $| α x + \frac{β x^{3}}{3} |_{0}^{1}$ $= α + \frac{β}{3} = 5$

Given $α$ = 1

So, $\frac{β}{3} = 4 \Rightarrow β = 12 N / m^{2}$

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