137

You visited us 137 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Volume Stress

A capacitor o...

Question

A capacitor of capacitance $C = .015 F$ is connected to parallel conducting rail and a conducting rod of mass m= $100$ g and length $l = 1 m$ start the fall under gravity in vertical plane. A uniform magnetic field of $2 T$ exist in space direction perpendicular to rod as shown in figure. Find acceleration of rod.

6.25 m / s^{2}

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

1.69 m / s^{2}

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

1.44 m / s^{2}

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

2.25 m / s^{2}

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

Open in App

Solution

The correct option is A $6.25 m / s^{2}$
$\begin{matrix} E = B l V Q = C E = B l V C i = \frac{d Q}{d t} = B l C \frac{d V}{d t} \Rightarrow F_{b} = B i l = B . B l C (\frac{d V}{d t}) l = B^{2} l^{2} C (\frac{d V}{d t}) ∴ m g - B^{2} l^{2} C . a = m a \Rightarrow m g - (m + B^{2} l^{2} C) C \Rightarrow a = \frac{m g}{m + B^{2} l^{2} C} = \frac{1}{\frac{100}{1000} + 4 \times 1^{2} \times \frac{15}{1000}} = \frac{1000}{160} = 6.25 m / s^{2} \end{matrix}$

Hence,

option $A$ is correct answer.

Suggest Corrections

Similar questions

Q. A uniform rod of mass

m

and length

l = 1 m

is hinged to a cart in vertical position as shown in figure. If cart starts moving at acceleration

a = 2 m / s^{2}

. EMF induced(in volts) across rod when it becomes horizontal, if uniform magnetic field of B = 2T exist in space is

[g = 10 m / s^{2}]

Q. A uniform rod of mass

m

and length

l = 1 m

is hinged to a cart in vertical position as shown in figure. If cart starts moving at acceleration

a = 2 m / s^{2}

. EMF induced(in volts) across rod when it becomes horizontal, if uniform magnetic field of B = 2T exist in space is

[g = 10 m / s^{2}]

Q. As shown in figure, two vertical conducting rails separated by distance

1.0 m

are placed parallel to z-axis. At

z = 0

, a capacitor of

0.15 F

is connected between the rails and a metal rod of mass

100 g m

placed across the rails slides down along the rails. If a constant magnetic fields of

2.0 T

exists perpendicular to the plane of the rails, what is the acceleration of the rod?
(Take

g = 9.8 m / s^{2})

Q. A conducting rod

M N

of mass

^{'} m

and length

^{'} ℓ^{'}

is placed on parallel smooth conducting rails connected to an uncharged capacitor of capacitance

^{'} C^{'}

and a battery of emf

ε

as shown. A uniform magnetic field

^{'} B^{'}

is existing perpendicular to the plane of the rails.The steady state velocity acquired by the conducting rod

M N

after closing switch

S

is (neglect the resistance of the parallel rails and the conducting rod )

Q. A copper wire

a b

of length

l

, resistance

r

and mass

m

starts sliding at

t = 0

down a smooth, vertical, thick pair of connected conducting rails as shown in figure. A uniform magnetic field

B

exists in the space in a direction perpendicular to the plane of the rails. Choose the correct option(s).

Join BYJU'S Learning Program

A capacitor of capacitance C=.015F is connected to parallel conducting rail and a conducting rod of mass m=100g and length l=1m start the fall under gravity in vertical plane. A uniform magnetic field of 2T exist in space direction perpendicular to rod as shown in figure. Find acceleration of rod.

The correct option is A 6.25m/s2 E=BlVQ=CE=BlVCi=dQdt=BlCdVdt⇒Fb=Bil=B.BlC(dVdt)l=B2l2C(dVdt)∴mg−B2l2C.a=ma⇒mg−(m+B2l2C)C⇒a=mgm+B2l2C=11001000+4×12×151000=1000160=6.25m/s2 Hence, option A is correct answer.