SATHEE: Work Energy And Power Question 139

Work Energy And Power Question 139

Question: A particle of mass m moves along a circular path of radius r with centripetal acceleration $a_{n}$ changing with time t as $a_{n} = k t^{2}$ , where k is-a positive constant. The average power developed by all the forces acting on the particle during the first $t_{0}$ seconds is

Options:

A) $m k r t_{0}$

B) $\frac{m k r t_{0}^{2}}{2}$

C) $\frac{m k r t_{0}^{}}{2}$

D) $\frac{m k r t_{0}^{}}{4}$

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Given $a_{n} = k t^{2}$

Or $\frac{v^{2}}{r} = k t^{2}$

or $v^{2} = k r t^{2}$ Therefore, average power delivered = $\frac{T o t a l w o r k d o n e}{T o t a l t i m e e l a p e d}$

$= \frac{i n c r e a s e i n K E}{T o t a l t i m e e l a p s e d}$

Or $= \frac{\frac{1}{2} m (v^{2} - 0^{2})}{t_{0}} = \frac{m}{2} \frac{k r t_{0}^{2}}{t_{0}} = \frac{m k r t_{0}^{2}}{2}$

Alternative: $v = \sqrt{k r t} \Rightarrow a_{t} = \sqrt{k r}$

$P = F_{t} v = m a_{t} v = m k r t$

$= \frac{\int_{0}^{t_{0}} P d t}{t_{0}} = \frac{1}{2} m k r t_{0}^{2}$

Work Energy And Power Question 139

Question: A particle of mass m moves along a circular path of radius r with centripetal acceleration $a_{n}$ changing with time t as $a_{n} = k t^{2}$ , where k is-a positive constant. The average power developed by all the forces acting on the particle during the first $t_{0}$ seconds is

Options:

Answer:

Solution:

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Work Energy And Power Question 139

Question: A particle of mass m moves along a circular path of radius r with centripetal acceleration an changing with time t as an=kt2 , where k is-a positive constant. The average power developed by all the forces acting on the particle during the first t0 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 along a circular path of radius r with centripetal acceleration $a_{n}$ changing with time t as $a_{n} = k t^{2}$ , where k is-a positive constant. The average power developed by all the forces acting on the particle during the first $t_{0}$ seconds is