SATHEE: Kinematics Question 486

Kinematics Question 486

Question: A particle of mass $m$ is moving in a circular path of constant radius $r$ such that it’s centripetal acceleration $a_{c}$ it’s varying with time t as, $a_{c} = k^{2} r t^{2}$ , The power delivered to the particle by the forces acting on it’s[IIT 1994]

Options:

A) $2 π m k^{2} r^{2} t$

B) $m k^{2} r^{2} t$

C) $\frac{m k^{4} r^{2} t^{5}}{3}$

D) Zero

Show Answer

Answer:

Correct Answer: B

Solution:

Here the tangential acceleration also ex it’s which requires power.

Given that $a_{C} = k^{2} r t^{2}$ and $a_{C} = \frac{v^{2}}{r}$ $\frac{v^{2}}{r} = k^{2} r t^{2}$

or $v^{2} = k^{2} r^{2} t^{2}$ or $v = k r t$

Tangential acceleration $a = \frac{d v}{d t} = k r$

Now force $F = m \times a = m k r$

So power $P = F \times v = m k r \times k r t = m k^{2} r^{2} t$

Kinematics Question 486

Question: A particle of mass $m$ is moving in a circular path of constant radius $r$ such that it’s centripetal acceleration $a_{c}$ it’s varying with time t as, $a_{c} = k^{2} r t^{2}$ , The power delivered to the particle by the forces acting on it’s[IIT 1994]

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

Kinematics Question 486

Question: A particle of mass m is moving in a circular path of constant radius r such that it’s centripetal acceleration ac it’s varying with time t as, ac=k2rt2 , The power delivered to the particle by the forces acting on it’s[IIT 1994]

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

Menu

Question: A particle of mass $m$ is moving in a circular path of constant radius $r$ such that it’s centripetal acceleration $a_{c}$ it’s varying with time t as, $a_{c} = k^{2} r t^{2}$ , The power delivered to the particle by the forces acting on it’s[IIT 1994]