Question 14 Marks
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SECTION - B [PHYSICS - NUMERIC]
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Question 24 Marks
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Question 34 Marks
Two coherent monochromatic light beams of intensities 4 I and 9 I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of $x$ is __________.
Answer
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$
\begin{array}{l}
I_{\max }=\left(\sqrt{I_1}+\sqrt{I_2}\right)^2 \\
=(\sqrt{4 I}+\sqrt{9 I})^2=25 I \\
I_{\min }=\left(\sqrt{I_1}-\sqrt{I_2}\right)^2 \\
=(\sqrt{4 I}-\sqrt{9 I})^2=I \\
I_{\max }-I_{\min }=24 I \\
x=24
\end{array}
$
$
\begin{array}{l}
I_{\max }=\left(\sqrt{I_1}+\sqrt{I_2}\right)^2 \\
=(\sqrt{4 I}+\sqrt{9 I})^2=25 I \\
I_{\min }=\left(\sqrt{I_1}-\sqrt{I_2}\right)^2 \\
=(\sqrt{4 I}-\sqrt{9 I})^2=I \\
I_{\max }-I_{\min }=24 I \\
x=24
\end{array}
$
Question 44 Marks
A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to an uniform magnetic field of strength 0.15 T . The magnetic force on the wire is __________ mN.
Answer
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$F = I \ell B$
$
\begin{array}{l}
=8 \times \frac{4}{100} \times 0.15 \\
=48 \times 10^{-3} N=48 mN
\end{array}
$
$F = I \ell B$
$
\begin{array}{l}
=8 \times \frac{4}{100} \times 0.15 \\
=48 \times 10^{-3} N=48 mN
\end{array}
$
Question 54 Marks
Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time $T =4$ seconds. If the sides of the triangle are increased to length $2 a$ and also the masses of the spheres are made 2 m , then they will collide after __________ seconds.
Answer
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$
T \propto m^{x} G^{y} a^{z}
$
$
\begin{array}{l}
T \propto M^{x}\left[M^{-1} L^3 T^{-2}\right]^y[L]^z \\
T \propto M^{x-y} L^{3 y+z} T^{-2 y} \\
x-y=0 \Rightarrow x=y \\
-2 y=1 \Rightarrow y=-\frac{1}{2}, x=-\frac{1}{2} \\
\Rightarrow 3 y+z=0 \\
z=-3 y=\frac{3}{2}
\end{array}
$
Hence
$
\begin{array}{l}
T \propto m^{-1 / 2} G^{-1 / 2} a^{3 / 2} \\
T \propto\left(\frac{a^3}{m}\right)^{1 / 2} \\
T=4 \times\left(\frac{2^3}{2}\right)^{1 / 2}=8 s
\end{array}
$
$
T \propto m^{x} G^{y} a^{z}
$
$
\begin{array}{l}
T \propto M^{x}\left[M^{-1} L^3 T^{-2}\right]^y[L]^z \\
T \propto M^{x-y} L^{3 y+z} T^{-2 y} \\
x-y=0 \Rightarrow x=y \\
-2 y=1 \Rightarrow y=-\frac{1}{2}, x=-\frac{1}{2} \\
\Rightarrow 3 y+z=0 \\
z=-3 y=\frac{3}{2}
\end{array}
$
Hence
$
\begin{array}{l}
T \propto m^{-1 / 2} G^{-1 / 2} a^{3 / 2} \\
T \propto\left(\frac{a^3}{m}\right)^{1 / 2} \\
T=4 \times\left(\frac{2^3}{2}\right)^{1 / 2}=8 s
\end{array}
$