Question

1) Two satellite of mass 'M' and '5M' are revolving around the sun in the same orbit. The ratio of their periods of revolution is
a) 4:1
b) 1:2
c) 2:1
d) 1:1

2) A bar magnet is of geometric length 12cm. its magnetic length will be
a) 0.1m
b) 0.12m
c) 0.144m
d) 0.2m

3) Which one of the following is NOT the SI unit of magnetic field?
a) N / Am
b) Wb / m²
c) NAm
d) tesla​

Answer 1

1) d) 1:1

2) a) 0.1m

3) c) NAm

1) From Kepler's law,

$T^{2}$ is directly proportional to $R^{3}$

Since,

$T^{2} = \frac{4\pi ^{2} R^{3} }{GM_{P} }$

Here, mass of satellite is nowhere related to Time periods of revolution around sun.

Since, the radii are same the ratio will be 1:1.

2) Since, magnetic length of bar magnet is approximately 80% of its geometric length.

80% of 12cm = $\frac{80(0.12)}{100}$ = 0.096 = 0.1 (approximately).

Therefore, option A with 0.1m is correct.

3)Since, $\frac{Wb}{m^{2} }$ and Tesla are SI units of magnetic field. Therefore, NAm is not the unit of magnetic field.

Answer 2

Answer:

1) d) 1:1

2) a) 0.1m

3) c) NAm

Explanation:

1) Here we have been mentioned that two satellites of different masses M and 5M are revolving around the sun in the same orbit.

The formula for a period of revolution is as follows;

$T^{2} = \frac{4\pi^{2}R^{3} }{GM_{p} }$

Here T is the time period of the revolution, R is the radius of the planet, G is the universal gravitation constant, and $M_{p}$ is the mass of the planet around which the satellite is revolving.

As here we can see that the period of revolution does not depends or vary with the mass of the satellite hence the period of revolution of both the satellites will be equal and hence their ratio will be 1:1

Therefore option d) 1:1 is correct.

2) We know that the magnetic length of the bar magnet is $\frac{5}{6}$ times the geometric length.

So here we have been given that geometric length is 12 cm therefore magnetic length is calculated as follows:

Magnetic length = $\frac{5}{6}$ × 12 cm

= 5 × 2 cm

= 10 cm

Now as we know that 100 cm = 1m

= 10 cm ÷ 100

= 0.1 m

Hence the magnetic length of the bar magnet is found to be 0.1 m

Therefore option a)0.1 m is correct.

3) The S.I unit of the respective magnetic field is Tesla(T).

1 Tesla can also be written as N / Am or Wb / $m^{2}$ But it cannot be written as NAm

Therefore option c) NAm is not the S.I unit of the magnetic field.