A force F -3 ti i -5 j - acts on body due to which its displacement varies as s -2 t 2 i i -5 j - Work done by this force in t -0 to 2 sec isA- 23 JB- 35 JC- 32 JD- zero

The correct option is C 32 JGiven, F→=3ti^+5j^ s→=2t2i^ 5j^ ds→dt=4ti^ w=∫F→.ds→=∫02(3ti^+5j^).(4ti^)dt nbsp; nbsp; nbsp; nbsp;=∫0212t2dt=4(23 02)=32 ...

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Byju's Answer

Standard XII

Mathematics

Standard Formulae - 1

A force F →=3...

Question

A force $\to F = (3 t ˆ i + 5 ˆ j)$ acts on body due to which its displacement varies as $\to s = (2 t^{2} ˆ i - 5 ˆ j)$ . Work done by this force in $t = 0$ to $2 s e c$ is

23 J

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32 J

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zero

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35 J

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Solution

The correct option is B $32 J$
Given,
$\to F = 3 t ˆ i + 5 ˆ j$
$\to s = 2 t^{2} ˆ i - 5 ˆ j$

$\frac{d \to s}{d t} = 4 t ˆ i$
$w = \int \to F . d \to s = \int_{0}^{2} (3 t ˆ i + 5 ˆ j) . (4 t ˆ i) d t = \int_{0}^{2} 12 t^{2} d t = 4 (2^{3} - 0^{2}) = 32 J$

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Q. A force

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\to s = (2 t^{2} ˆ i - 5 ˆ j)

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A force →F=(3tˆi+5ˆj) acts on body due to which its displacement varies as →s=(2t2ˆi−5ˆj). Work done by this force in t=0 to 2sec is

The correct option is B 32 JGiven, →F=3tˆi+5ˆj →s=2t2ˆi−5ˆj d→sdt=4tˆi w=∫→F.d→s=∫20(3tˆi+5ˆj).(4tˆi)dt =∫2012t2dt=4(23−02)=32 J

A force $\to F = (3 t ˆ i + 5 ˆ j)$ acts on body due to which its displacement varies as $\to s = (2 t^{2} ˆ i - 5 ˆ j)$ . Work done by this force in $t = 0$ to $2 s e c$ is

The correct option is B $32 J$
Given,
$\to F = 3 t ˆ i + 5 ˆ j$
$\to s = 2 t^{2} ˆ i - 5 ˆ j$

$\frac{d \to s}{d t} = 4 t ˆ i$
$w = \int \to F . d \to s = \int_{0}^{2} (3 t ˆ i + 5 ˆ j) . (4 t ˆ i) d t = \int_{0}^{2} 12 t^{2} d t = 4 (2^{3} - 0^{2}) = 32 J$