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Laws of Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsLaws of Motion1 Mark
MCQ
A body with mass $5\ kg$ is acted upon by a force $\text{F}=(-3\hat{\text{i}}+4\hat{\text{j}})\text{N.}$ If its initial velocity at $t = 0$ is $\text{v}=(6\hat{\text{i}}-12\hat{\text{j}})\text{m s}^{-1},$ the time at which it will just have a velocity along the $y-$axis is:
  • A
    never
  • ✓
    $10s$
  • C
    $2s$
  • D
    $15s$
✓

Answer

Correct option: B.
$10s$
According to the problam, mass $m = 5\ kg$
Force which is acting uppon the block $\vec{\text{F}}=(-3\hat{\text{i}}+4\hat{\text{j}})\text{N}$
Inital velocity at $\text{t}=0,\ \vec{\text{u}}=(6\vec{\text{i}}-12\vec{\text{j}})\text{m/s}$
Retardation, $\vec{\text{a}}=\frac{\vec{\text{F}}}{\text{m}}=\Big(-\frac{3\vec{\text{i}}}{5}+\frac{4\vec{\text{j}}}{5}\Big)\text{m/s}^2$
And when final veocity is along $y-$axis only, its $x-$componet must be zero.
We have to apply kinematic wquations seprately for $x-$component only. then we get $\text{v}_\text{x}=\text{u}_\text{x}+\text{a}_\text{x}\text{t}$
$0= 6\vec{\text{i}}-\frac{3\vec{\text{i}}}{5}\text{t}$
$\text{t}=\frac{5\times6}{3}=10\ \text{s}$

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