A particle is displaced from 1- 2 m to 0- 0 m along the path y-2x3- Work done by a force F-x3 -y - N acting on the particle- during this displacement is in J-Give your answer without considering sign-

Given F=(x^3 ĵ+y î) N Work done by variable force is W=∫F. dr=∫ x^3 dy+∫ y dx W=∫_2^0y2 dy+∫_1^0 2x^3 dx W=12 ( y^22 )_2^0+2 ( x^44 )_1^0= 1.5 J Accepted answe ...

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Standard XII

Physics

Electric Field

A particle is...

Question

A particle is displaced from $(1, 2) m$ to $(0, 0) m$ along the path $y = 2 x^{3}$ . Work done by a force $\to F = (x^{3}^j + y^i) N$ acting on the particle, during this displacement is (in $J$ )

[Give your answer without considering sign]

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Solution

Given $F = (x^{3}^j + y^i) N$
Work done by variable force is
$W = \int \to F . \to d r = \int x^{3} d y + \int y d x$
$W = 0 \int 2 \frac{y}{2} d y + 0 \int 1 2 x^{3} d x$
$W = \frac{1}{2} {(\frac{y^{2}}{2})}_{2}^{0} + 2 {(\frac{x^{4}}{4})}_{1}^{0} = - 1.5 J$

Accepted answers : $1.5, 1.50, 1.500$

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Electric Field

Standard XII Physics

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A particle is displaced from (1,2) m to (0,0) m along the path y=2x3. Work done by a force →F=(x3^j+y^i) N acting on the particle, during this displacement is (in J) [Give your answer without considering sign]

Given F=(x3^j+y^i) N Work done by variable force is W=∫→F.→dr=∫x3dy+∫ydx W=0∫2y2dy+0∫12x3dx W=12(y22)02+2(x44)01=−1.5 J Accepted answers :1.5 , 1.50 , 1.500

A particle is displaced from $(1, 2) m$ to $(0, 0) m$ along the path $y = 2 x^{3}$ . Work done by a force $\to F = (x^{3}^j + y^i) N$ acting on the particle, during this displacement is (in $J$ )

[Give your answer without considering sign]

Given $F = (x^{3}^j + y^i) N$
Work done by variable force is
$W = \int \to F . \to d r = \int x^{3} d y + \int y d x$
$W = 0 \int 2 \frac{y}{2} d y + 0 \int 1 2 x^{3} d x$
$W = \frac{1}{2} {(\frac{y^{2}}{2})}_{2}^{0} + 2 {(\frac{x^{4}}{4})}_{1}^{0} = - 1.5 J$

Accepted answers : $1.5, 1.50, 1.500$