A particle moves along X -axis from x=0 to x=5 ~cm under the influence of force given by F= (7-2 x+3 x^2 ) N . The work done in the process is

Correct answer: (D) 135 J. The given force varies with distance. Therefore, work done, W=∫_0^x=5 F · d x =∫_0^5 (7-2 x+3 x^2 ) d x = [7 x-(2 x^2)/2+(3 x^3)/3 ]_0^5 = [7 × 5-(5)^2+(5)^3-0 ] =135 ~J

Q148 / 170 · Manipal (MET) 2016 · Physics

A particle moves along $X$-axis from $x=0$ to $x=5 \mathrm{~cm}$ under the influence of force given by $F=\left(7-2 x+3 x^2\right) \mathrm{N}$. The work done in the process is

A
70 J
B
270 J
C
35 J
Correct answer
D
135 J

Solution

The given force varies with distance. Therefore, work done, $W=\int_0^{x=5} F \cdot d x$ $\begin{aligned} & =\int_0^5\left(7-2 x+3 x^2\right) d x \\ & =\left[7 x-\frac{2 x^2}{2}+\frac{3 x^3}{3}\right]_0^5\end{aligned}$ $\begin{aligned} & =\left[7 \times 5-(5)^2+(5)^3-0\right] \\ & =135 \mathrm{~J}\end{aligned}$

Hence, the correct answer is option: 'D'.

A particle moves along $X$-axis from $x=0$ to $x=5 \mathrm{~cm}$ under the influence of force given by $F=\left(7-2 x+3 x^2\right) \mathrm{N}$. The work done in the process is

Solution

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