You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Thermal Expansion

A spring and ...

Question

A spring and block are shown in figure. When the block is pulled out to $x = + 4 c m$ , we must apply a force of magnitude $360 N$ to hold it there. We pull the block to $x = 11 c m$ and then release it. How much work does the spring do on the block as the block moves from $x = + 5 c m$ to $x = + 3 c m$ ?

720 Joules

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

7.2 Joules

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

7200 Joules

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

3600 Joules

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

Open in App

Solution

The correct option is B
7.2 Joules

When it is pulled out to x = 4 cm
$\Rightarrow$ F = kx
$\Rightarrow$ K = $\frac{360}{4 c m} = 9000 N / m$
$∴$ Work done by the spring, W = $\int d W = \int_{x_{2}}^{x_{1}} k x d x = - K {[\frac{x^{2}}{2}]}_{5}^{3} = - \frac{k}{2} [3^{2} - 5^{2}] \times 10^{- 4} = - \frac{9 \times 10^{3}}{2} \times 10^{- 4} [- 16] = 7.2 J$

Suggest Corrections

Similar questions

Q. A child applies a force

F

parallel to the

x

-axis to a block moving on a horizontal surface. The

x

-component of the force varies with the

x

-coordinate of the block as shown in figure. The work done by the force

F

when the block moves from

x = 0

x = 7 m

and

x = 3 m

4 m

are (in joules)

Q. A child applies a force

F

parallel to the

x

-axis to a block moving on a horizontal surface. The

x

-component of the force varies with the

x

-coordinate of the block as shown in figure. The work done by the force

F

when the block moves from

x = 0

x = 7 m

and

x = 3 m

4 m

are (in joules)

Q. A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in the figure. Initially, the spring is in the natural state. Then the maximum positive work that the applied force

F

can do is: (Given that spring does not break)

Q. A block whose mass is

1 k g

is fastened to a spring. The spring has a spring constant of

50 {N m}^{- 1}

. The block is pulled to a distance of

x = 10 c m

from its equilibrium position at

x = 0

c m

on a frictionless surface from rest at

t = 0

. The kinetic energy of the block when it is

5 c m

away from the mean position is

Q. The block shown in the figure, is acted on by a spring with spring constant

k

and a weak frictional force of constant magnitude

f

. The block is pulled a distance

x_{0}

from equilibrium position and then released. It oscillates many times and ultimately comes to rest. Find the number of cycles the mass oscillates before coming to rest :

Join BYJU'S Learning Program

A spring and block are shown in figure. When the block is pulled out to x=+4 cm, we must apply a force of magnitude 360 N to hold it there. We pull the block to x=11 cm and then release it. How much work does the spring do on the block as the block moves from x=+5 cm to x=+3 cm?

The correct option is B 7.2 Joules When it is pulled out to x = 4 cm ⇒ F = kx ⇒ K = 3604cm=9000N/m ∴ Work done by the spring, W = ∫dW=∫x1x2kxdx=−K[x22]35=−k2[32−52]×10−4=−9×1032×10−4[−16]=7.2 J