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PHXII05:MAGNETISM and MATTER

360422 Rate of change of torque $τ$ with deflection $θ$ is maximum for a magnet suspended freely in a uniform magnetic field of induction $B$ , when

1

θ = 0^{\circ}

2

θ = 45^{\circ}

3

θ = 60^{\circ}

4

θ = 90^{\circ}

Explanation:

As $t = M B \sin θ$
$\frac{d τ}{d θ} = M B \cos θ$
It will be maximum, when $θ = 0^{\circ}$ .

PHXII05:MAGNETISM and MATTER

360423 A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by $60^{\circ}$ is $W$ . Now the torque required to keep the magnet in this new position is

1

\frac{W}{\sqrt{3}}

2

\sqrt{3} W

3

\frac{\sqrt{3} W}{2}

4

\frac{2 W}{\sqrt{3}}

Explanation:

$W = - M B \cos 60^{o} - (- M B) \Rightarrow W = \frac{M B}{2}$
$∴ τ = M B \sin 60^{\circ} = 2 W \frac{\sqrt{3}}{2} = \sqrt{3} W$

NEET - 2016

PHXII05:MAGNETISM and MATTER

360424 Torques $τ_{1}$ and $τ_{2}$ , are required for magnetic needle to remain perpendicular to the magnetic fields and at two different places. The ratio is:

1

\frac{τ_{1}}{τ_{2}}

2

\frac{τ_{2}}{τ_{1}}

3

\frac{τ_{1} - τ_{2}}{τ_{1} - τ_{2}}

4

\frac{τ_{1} + τ_{2}}{τ_{1} - τ_{2}}

Explanation:

Torque, $τ = M B \sin θ$
$τ_{1} = M B_{1} \sin 90^{\circ} = M B_{1}$
and $τ_{2} = M B_{2} \sin 90^{\circ} = M B_{2}$
$\Rightarrow \frac{M B_{1}}{M B_{2}} = \frac{τ_{1}}{τ_{2}} \Rightarrow \frac{B_{1}}{B_{2}} = \frac{τ_{1}}{τ_{2}}$

PHXII05:MAGNETISM and MATTER

360425 A magnetic needle is placed on a cork floating in a still lake in the northern hemisphere. Does the needle together with the cork move towards the north of the lake?

1 Yes

2 No

3 May or may not move

4 Nothing can be said

PHXII05:MAGNETISM and MATTER

360422 Rate of change of torque $τ$ with deflection $θ$ is maximum for a magnet suspended freely in a uniform magnetic field of induction $B$ , when

1

θ = 0^{\circ}

2

θ = 45^{\circ}

3

θ = 60^{\circ}

4

θ = 90^{\circ}

Explanation:

As $t = M B \sin θ$
$\frac{d τ}{d θ} = M B \cos θ$
It will be maximum, when $θ = 0^{\circ}$ .

PHXII05:MAGNETISM and MATTER

360423 A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by $60^{\circ}$ is $W$ . Now the torque required to keep the magnet in this new position is

1

\frac{W}{\sqrt{3}}

2

\sqrt{3} W

3

\frac{\sqrt{3} W}{2}

4

\frac{2 W}{\sqrt{3}}

Explanation:

$W = - M B \cos 60^{o} - (- M B) \Rightarrow W = \frac{M B}{2}$
$∴ τ = M B \sin 60^{\circ} = 2 W \frac{\sqrt{3}}{2} = \sqrt{3} W$

NEET - 2016

PHXII05:MAGNETISM and MATTER

360424 Torques $τ_{1}$ and $τ_{2}$ , are required for magnetic needle to remain perpendicular to the magnetic fields and at two different places. The ratio is:

1

\frac{τ_{1}}{τ_{2}}

2

\frac{τ_{2}}{τ_{1}}

3

\frac{τ_{1} - τ_{2}}{τ_{1} - τ_{2}}

4

\frac{τ_{1} + τ_{2}}{τ_{1} - τ_{2}}

Explanation:

Torque, $τ = M B \sin θ$
$τ_{1} = M B_{1} \sin 90^{\circ} = M B_{1}$
and $τ_{2} = M B_{2} \sin 90^{\circ} = M B_{2}$
$\Rightarrow \frac{M B_{1}}{M B_{2}} = \frac{τ_{1}}{τ_{2}} \Rightarrow \frac{B_{1}}{B_{2}} = \frac{τ_{1}}{τ_{2}}$

PHXII05:MAGNETISM and MATTER

360425 A magnetic needle is placed on a cork floating in a still lake in the northern hemisphere. Does the needle together with the cork move towards the north of the lake?

1 Yes

2 No

3 May or may not move

4 Nothing can be said

PHXII05:MAGNETISM and MATTER

360422 Rate of change of torque $τ$ with deflection $θ$ is maximum for a magnet suspended freely in a uniform magnetic field of induction $B$ , when

1

θ = 0^{\circ}

2

θ = 45^{\circ}

3

θ = 60^{\circ}

4

θ = 90^{\circ}

Explanation:

As $t = M B \sin θ$
$\frac{d τ}{d θ} = M B \cos θ$
It will be maximum, when $θ = 0^{\circ}$ .

PHXII05:MAGNETISM and MATTER

360423 A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by $60^{\circ}$ is $W$ . Now the torque required to keep the magnet in this new position is

1

\frac{W}{\sqrt{3}}

2

\sqrt{3} W

3

\frac{\sqrt{3} W}{2}

4

\frac{2 W}{\sqrt{3}}

Explanation:

$W = - M B \cos 60^{o} - (- M B) \Rightarrow W = \frac{M B}{2}$
$∴ τ = M B \sin 60^{\circ} = 2 W \frac{\sqrt{3}}{2} = \sqrt{3} W$

NEET - 2016

PHXII05:MAGNETISM and MATTER

360424 Torques $τ_{1}$ and $τ_{2}$ , are required for magnetic needle to remain perpendicular to the magnetic fields and at two different places. The ratio is:

1

\frac{τ_{1}}{τ_{2}}

2

\frac{τ_{2}}{τ_{1}}

3

\frac{τ_{1} - τ_{2}}{τ_{1} - τ_{2}}

4

\frac{τ_{1} + τ_{2}}{τ_{1} - τ_{2}}

Explanation:

Torque, $τ = M B \sin θ$
$τ_{1} = M B_{1} \sin 90^{\circ} = M B_{1}$
and $τ_{2} = M B_{2} \sin 90^{\circ} = M B_{2}$
$\Rightarrow \frac{M B_{1}}{M B_{2}} = \frac{τ_{1}}{τ_{2}} \Rightarrow \frac{B_{1}}{B_{2}} = \frac{τ_{1}}{τ_{2}}$

PHXII05:MAGNETISM and MATTER

360425 A magnetic needle is placed on a cork floating in a still lake in the northern hemisphere. Does the needle together with the cork move towards the north of the lake?

1 Yes

2 No

3 May or may not move

4 Nothing can be said

PHXII05:MAGNETISM and MATTER

360422 Rate of change of torque $τ$ with deflection $θ$ is maximum for a magnet suspended freely in a uniform magnetic field of induction $B$ , when

1

θ = 0^{\circ}

2

θ = 45^{\circ}

3

θ = 60^{\circ}

4

θ = 90^{\circ}

Explanation:

As $t = M B \sin θ$
$\frac{d τ}{d θ} = M B \cos θ$
It will be maximum, when $θ = 0^{\circ}$ .

PHXII05:MAGNETISM and MATTER

360423 A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by $60^{\circ}$ is $W$ . Now the torque required to keep the magnet in this new position is

1

\frac{W}{\sqrt{3}}

2

\sqrt{3} W

3

\frac{\sqrt{3} W}{2}

4

\frac{2 W}{\sqrt{3}}

Explanation:

$W = - M B \cos 60^{o} - (- M B) \Rightarrow W = \frac{M B}{2}$
$∴ τ = M B \sin 60^{\circ} = 2 W \frac{\sqrt{3}}{2} = \sqrt{3} W$

NEET - 2016

PHXII05:MAGNETISM and MATTER

360424 Torques $τ_{1}$ and $τ_{2}$ , are required for magnetic needle to remain perpendicular to the magnetic fields and at two different places. The ratio is:

1

\frac{τ_{1}}{τ_{2}}

2

\frac{τ_{2}}{τ_{1}}

3

\frac{τ_{1} - τ_{2}}{τ_{1} - τ_{2}}

4

\frac{τ_{1} + τ_{2}}{τ_{1} - τ_{2}}

Explanation:

Torque, $τ = M B \sin θ$
$τ_{1} = M B_{1} \sin 90^{\circ} = M B_{1}$
and $τ_{2} = M B_{2} \sin 90^{\circ} = M B_{2}$
$\Rightarrow \frac{M B_{1}}{M B_{2}} = \frac{τ_{1}}{τ_{2}} \Rightarrow \frac{B_{1}}{B_{2}} = \frac{τ_{1}}{τ_{2}}$

PHXII05:MAGNETISM and MATTER

360425 A magnetic needle is placed on a cork floating in a still lake in the northern hemisphere. Does the needle together with the cork move towards the north of the lake?

1 Yes

2 No

3 May or may not move

4 Nothing can be said