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Question 22 Marks
Define gravitational potential energy. Give its SI unit.
Answer
The amount of work required to transport a body of unit mass from infinity to some point is known as gravitational potential. The mathematical expression will be $G = Wm$.
The SI unit of gravitational potential is $JKg ^{-1}$
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Question 32 Marks
Why is the weight of a body at the poles more than the weight at the equator? Explain.
Answer
As $g =\frac{G M}{R^2}$ and the value of R at the poles is less than that at the equator, so g at poles is greater that g at the equator.
Now, as $g _{ p }> g _{ e }$, hence $mg _{ p }> mg _{ e }$
i.e., the weight of a body at the poles is more than the weight at the equator.
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Question 42 Marks
Why do the passengers fall in backward direction when a bus suddenly starts moving from the rest position?
Answer
When the bus suddenly starts moving, the lower part of the passenger's body begins to move along with the bus while the upper part tend to remain at rest due to inertia of rest. That is why a passenger standing or sitting loosely in a bus falls backward when the bus suddenly starts moving.
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Question 52 Marks
The wavelength $\lambda$ associated with a moving particle depends upon its mass m , its velocity v and Planck's constant h. Show dimensional relation between them.
Answer
Suppose wavelength $\lambda$ associated with a moving particle depends upon (i) its mass (m), (ii) its velocity (v) and (iii) Planck's constant (h), then
$
\lambda=k m^a v^b h^c . .(1)
$
where, k is a dimensionless constant.
Representing the above equation in terms of its dimensions, we get
$
\begin{aligned}
& {\left[M^0 L^1 T^0\right]=[M]^a\left[LT^{-1}\right]^{b}\left[ML^2 T^{-1}\right]^{c}} \\
& \Rightarrow\left[M^0 L^1 T^0\right]=M^{a+c} L^{b+2 c} T^{-b-c} . .(2)
\end{aligned}
$
Comparing power of $M , L$ and T on both sides of equation (2), we get
$
a+c=0, b+2 c=1,-b-c=0
$
we get $a=-1, b=-1, c=+1$
putting the value of $a, b$, and $c$ in equation (1), we get
$
\begin{aligned}
& \lambda=k m^{-1} v^{-1} h^1 \\
& \lambda=\frac{k h}{m v}
\end{aligned}
$
Hence, the relation becomes $\lambda=\frac{k h}{m v}$ and it gives the de broglie wavelength of a moving particle.
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Question 62 Marks
What are transverse waves? Give examples too.
Answer
Transverse waves are the waves in which the medium particles vibrate to and fro about their mean positions at right angles to the direction of wave propagation. Transverse waves travel in the form of crests and troughs. One crest and the adjoining trough constitute one wave.
A simple example is given by the waves that can be created on a horizontal length of string by anchoring one end and moving the other end up and down. Another example is the waves that are created on the membrane of a drum. The waves propagate in directions that are parallel to the membrane plane, but the membrane itself gets displaced up and down, perpendicular to that plane. Light is another example of a transverse wave, where the oscillations are the electric and magnetic fields, which point at right angles to the ideal light rays that describe the direction of propagation.
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