2 Marks Questions

Question 12 Marks

An astronaut, by mistake, drops his food packet from an artificial satellite orbiting around the earth. Will it reach the surface of the earth? Why?

Answer

The food packet will not fall on the earth. As the satellite, as well as an astronaut, were in a state of weightlessness hence, the food packet when dropped by mistake, will also start moving with the same velocity as that of satellite and will continue to move along with the satellite in the same orbit.

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Question 22 Marks

At a point above the surface of the earth, the gravitational potential is $-5.12 \times 10^7 J / kg$ and the acceleration due to gravity is $6.4 m / s ^2$. Assuming the mean radius of the earth to be 6400 km , calculate the height of the point above the earth's surface.

Answer

If $r$ is the distance of the given point from the centre of the earth, the gravitational potential at the point,
$
v=-\frac{G M}{r}=-5.12 \times 10^7 J / kg
$
Acceleration due to gravity at this point,
$
g=\frac{G M}{r^2}=6.4 m / s^2
$
Clearly, $\frac{|V|}{g}=\frac{G M / r}{G M / r^2}= r$
thus, $r=\frac{5.12 \times 10^7 J / kg }{6.4 m / s ^2}=8 \times 10^6 m=8000 km$
Obviously, height of the point from the earth's surface $=( r - R )=8000 km-6400 km=1600 km$

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Question 32 Marks

Is friction a non-conservative force?

Answer

Yes. When the direction of motion of a body reverses, the direction of friction is also reversed. Work has to be done against friction both during the forward and return journey i.e., work done against friction along a closed path is not zero. So friction is a non-conservative force.

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Question 42 Marks

The density of mercury is $13.6 g cm ^{-3}$ in CGS system. Find its value in SI units.

Answer

$\begin{aligned} & \text { [Density] }= M ^1 L^{-3} \\ & n _2= n _1\left[\frac{M_1}{M_2}\right]^1\left[\frac{L_1}{L_2}\right]^{-3} \\ & =13.6\left[\frac{1 g}{1 kg}\right]^1\left[\frac{1 cm}{1 m}\right]^{-3} \\ & =13.6\left[\frac{1 g}{1000 g}\right]\left[\frac{1 cm}{100 cm}\right]^{-3}=13.6 \times 10^3 \\ & \therefore 13.6 g cm ^{-3}=13.6 \times 10^3 kgm ^{-3}\end{aligned}$

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Question 52 Marks

Differentiate between dimensional and non-dimensional variables.

Answer

The quantities which have dimensions but do not possess a constant value are called dimensional variables e.g., velocity, force etc. On the other hand, the quantities which have neither dimensions nor they have a constant value are called non-dimensional variables e.g., relative density, strain, etc.

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Question 62 Marks

A stone is dropped into a well and its splash is heard at the mouth of the well after an interval of 1.45 s . Find the depth of the well. Given that velocity of sound in air at room temperature is equal to $332 ms^{-1}$.

Answer

Let $h$ be the depth of the well. Then time $t_1$ taken by the stone to fall into well under gravity is given by $h=0+\frac{1}{2} g t_1^2$ or $t _1=\sqrt{\frac{2 h}{g}}$
Time taken for the splash to travel height h is given by $t_2=\frac{h}{v}$
where $v=$ velocity of sound
But $t _1+ t _2=1.45 s$
$\therefore \quad \sqrt{\frac{2 h}{g}}+\frac{h}{v}=1.45$
or $\sqrt{\frac{2 h}{9.8}}+\frac{h}{332}=1.45$
On solving, $h =9.9 m$.

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