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BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Physics
Chapter
Laws of Motion

BITSAT 2023 · Paper 1 · Physics · Laws of Motion

At any instant the velocity of a particle of mass 500 ~g is (2 t i...

At any instant the velocity of a particle of mass 500 g500 \mathrm{~g} is \left(2 t \hat{i}+3 t^2 \hat{j}\right) \mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm{ms}^{-1}.Iftheforceactingontheparticleat. If the force acting on the particle att=1 sisis(\hat{i}+x \hat{j}) N.Thenthevalueof. Then the value of\mathrm{x}$ will be:

Options

  1. A3
  2. B4
  3. C6
  4. D2

Correct answer

A. 3

Step-by-step solution

Mass of particle, m=500g=0.5kg\mathrm{m}=500 \mathrm{ g}=0.5 \mathrm{ kg}
velocity of a particle, v⃗=2ti^+3t2j^\vec{v}=2 t \hat{i}+3 t^2 \hat{j}
a→=dv→dt=2i^+6tj^\overrightarrow{\mathrm{a}}=\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}=2 \hat{\mathrm{i}}+6 \mathrm{t} \hat{\mathrm{j}}
at t=1,a→=2i^+6j^\mathrm{t}=1, \overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}
Force acting on the particle,
F→=ma=0.5(2i^+6j^)=i^+3j^\overrightarrow{\mathrm{F}}=\mathrm{ma}=0.5(2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}})=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}
F→=i^+xj^\overrightarrow{\mathrm{F}}=\hat{\mathrm{i}}+x \hat{\mathrm{j}} \quad Hence x=3x=3
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