A particle of mass is driven by a machine that delivers a constant power watts. If the particle starts from rest, the force on the particle at time is [2015]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

Q.
A particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest, the force on the particle at time $t$ is [2015]

1 $\sqrt{2 m k} t^{- 1 / 2}$

2 $\frac{1}{2} \sqrt{m k} t^{- 1 / 2}$

3 $\sqrt{\frac{m k}{2}} t^{- 1 / 2}$

4 $\sqrt{m k} t^{- 1 / 2}$

Ans.
(3)

Constant power acting on the particle of mass $m$ is $k$ watt.

or $P = k; \frac{d W}{d t} = k; d W = k d t$

Integrating both sides, $\int_{0}^{W} d W = \int_{0}^{t} k$ $d t$

$\Rightarrow W = k t$ ...(i)

Using work-energy theorem,

$W = \frac{1}{2} m v^{2} - \frac{1}{2} m {(0)}^{2} \Rightarrow k t = \frac{1}{2} m v^{2} [Using (i)]$

$v = \sqrt{\frac{2 k t}{m}}$

Acceleration of the particle, $a = \frac{d v}{d t}$

$a = \frac{1}{2} \sqrt{\frac{2 k}{m}}$ $\frac{1}{\sqrt{t}} = \sqrt{\frac{k}{2 m t}}$

Force on the particle, $F = m a = \sqrt{\frac{m k}{2 t}} = \sqrt{\frac{m k}{2}} t^{- 1 / 2}$

Solution

Q.
A particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest, the force on the particle at time $t$ is [2015]

1 $\sqrt{2 m k} t^{- 1 / 2}$

2 $\frac{1}{2} \sqrt{m k} t^{- 1 / 2}$

3 $\sqrt{\frac{m k}{2}} t^{- 1 / 2}$

4 $\sqrt{m k} t^{- 1 / 2}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest, the force on the particle at time t is [2015]

1 2mkt-1/2

2 12mkt-1/2

3 mk2t-1/2

4 mkt-1/2

Want Us to Email you About Special Offers & Updates?

Q.
A particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest, the force on the particle at time $t$ is [2015]

1 $\sqrt{2 m k} t^{- 1 / 2}$

2 $\frac{1}{2} \sqrt{m k} t^{- 1 / 2}$

3 $\sqrt{\frac{m k}{2}} t^{- 1 / 2}$

4 $\sqrt{m k} t^{- 1 / 2}$