Magnitude of work done by gravity during the motion of system is

0.8 J

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1.6 J

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0.4 J

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 J

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $1.6 J$
Due to weight of block m, let spring gets elongated by distance $x$ .
As one end of the rope is fixed , the block of mass m will go down by distance $2 x$ .
Given:
Initial Velocity $u = 0$ and at maximum extension
spring will come to rest for a moment so final Velocity $v = 0$ .
change in kinetic energy $Δ K E = \frac{1}{2} m v^{2} - \frac{1}{2} m u^{2}$
$Δ K E = 0$

From work energy theorem , it is known

$Δ K E = W_{g} + W_{f} + W_{s}$ , where $W_{g}$ is work done by gravity,
$W_{f}$ is work done by friction on block of mass $2 m$ and $W_{s}$ is work done by spring.
$W_{g} = m g \times 2 x = 1 \times 10 \times 2 x = 20 x$

$W_{s} = - \frac{1}{2} k x^{2} = - 0.5 \times 100 x^{2} = - 50 x^{2}$

$W_{f} = - μ 2 m g x = - 0.8 \times 2 \times 10 x = - 16 x$

putting values in

$Δ K E = W_{g} + W_{f} + W_{s}$

$0 = 20 x - 50 x^{2} - 16 x$

$50 x^{2} - 4 x = 0$

$x = 0.08 m$

$x = 80 c m$

work done by gravity
$W_{g} = m g \times 2 x = 1 \times 10 \times 2 \times 0.08 = 1.6 J$

Suggest Corrections

Similar questions

Q. Consider that the system shown below is released from rest. The work done by force of gravity during first

2

seconds of the motion is (Take

g = 10 m s^{- 2}

)

Q. The work done by gravity during the descent of a projectile:

The two blocks in an Atwood machine have masses 2.0 kg and 3.0 kg. Find the work done by gravity during the fourth second after the system is released from rest.

Q. Work done by normal reaction is zero during the motion of the block:

Q. A system works in a cylic process. It absorbs 20 calories of heat and rejects 60 J of heat during the process. The magnitude of work done (J) is (1 calorie = 4.2 J) :

Join BYJU'S Learning Program