SATHEE: Work Energy And Power Question 137

Work Energy And Power Question 137

Question: A particle of mass $m$ moves with a variable velocity $v$ , which changes with distance covered $x$ along a straight line as $v = k \sqrt{x}$ , where A: is a positive constant. The work done by all the forces acting on the particle, during the first $t$ seconds is

Options:

A) $\frac{m k^{4}}{t^{2}}$

B) $\frac{m k^{4} t^{2}}{4}$

C) $\frac{m k^{4} t^{2}}{8}$

D) $\frac{m k^{4} t^{2}}{16}$

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Given $v = k \sqrt{x}$ Or $\frac{d x}{d t} = k \sqrt{x}$

or $x^{\frac{1}{2}} d x = k d t$

Integrating both sides, we get $\frac{x^{\frac{1}{2}}}{\frac{1}{2}} = k t + C;$

Assuming $x (0) = 0$ Therefore, $C = 0$

$2 \sqrt{x} = k t \Rightarrow x = \frac{k^{2} t^{2}}{4}$

or $v = \frac{k^{2} t}{2}$

Therefore, work done, $Δ W =$ Increase in KE $= \frac{1}{2} m v^{2} - \frac{1}{2} m {(0)}^{2} = \frac{1}{2} m {[\frac{k^{2} t}{2}]}^{2} = \frac{1}{8} m k^{4} t^{2}$

Work Energy And Power Question 137

Question: A particle of mass $m$ moves with a variable velocity $v$ , which changes with distance covered $x$ along a straight line as $v = k \sqrt{x}$ , where A: is a positive constant. The work done by all the forces acting on the particle, during the first $t$ seconds is

Options:

Answer:

Solution:

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Work Energy And Power Question 137

Question: A particle of mass m moves with a variable velocity v , which changes with distance covered x along a straight line as v=kx , where A: is a positive constant. The work done by all the forces acting on the particle, during the first t seconds is

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: A particle of mass $m$ moves with a variable velocity $v$ , which changes with distance covered $x$ along a straight line as $v = k \sqrt{x}$ , where A: is a positive constant. The work done by all the forces acting on the particle, during the first $t$ seconds is