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A uniform thin rope of length $12\text{m}$ and mass $6\text{kg}$ hangs vertically from a rigid support and a block of mass $2\text{kg}$ is attached to its free end. A transverse short wave-train of wavelength $6\text{cm}$ is produced at the lower end of the rope. What is the wavelength of the wave train (in$\text{cm}$) when it reaches the top of the rope?

In the system shown in the figure $m_1>m_2$. System is held at rest by thread $BC$. Just after the thread $BC$ is cut:



(A) Acceleration of $m_2$ will be upwards

(B) Magnitude of acceleration of both blocks will be equal to $\left(\frac{m_1-m_2}{m_1+m_2}\right)g$

(C) Acceleration of $m_1$ will be equal to zero

(D) Magnitude of acceleration of two blocks will be non-zero and unequal.

From the above four statements we can conclude

A bomb of mass 1 kg initially at rest, explodes and breaks into three fragments of masses in the ratio 1:1:3. The two pieces of equal masses fly off perpendicular to each other with a speed 15 m/s each. What will be the speed of heavier fragment ?

A long solenoid has $50$ turns per meter of its length. If a current of $5\text{A}$ is passed through it, then the magnetic field at the end of the solenoid will be nearly equal to



​​​​​​​$[$0.77 Mark$]$

A coil has resistance of $6\Omega$ & inductance of $0.08H$. It is connected with alternating voltage of $250V,\frac{50}{\pi }Hz.$ The average power consumed in circuit

All properties of the charge

If the initial velocity of $m_1$ is $um{s}^{-1}$ and initial velocity of $m_2$ is $2um{s}^{-1}$. After collision $m_2$ stops, then what is the final velocity of $m_1$ after collision? If $m_1$ = $mkg$ and $m_2$ = $2mkg$.

The magnetic bearing of a line AB is S ${45}^{\circ }$ E and the declination is $5^{\circ }$ West. The true bearing of the line AB is

Find out the distance of the point where the incident ray intersects the principal axis from the pole of the mirror.

In $L-C$ oscillation circuit if the frequency of oscillation of charge is $f$, then the frequency of oscillation of magnetic energy is

Define self inductance of a coil. Mention the factors on which it depends.

A body $A$ starts from rest with an acceleration $a_A$. After 2 seconds, another body $B$ starts from rest with an acceleration $a_B$. If they travel equal distances in the $5^{th}$ second, after the start of $A$, then the ratio $a_A:a_B$ is equal to

An LED is constructed from a pn junction based on a certain semi-conducting material whose energy gap is 1.9 eV. Then the wavelength of the emitted light is

In the circuit in figure, if no current flows through the galvanometer when the key is closed, the bridge is balanced. The balancing condition for bridge is.

For a point outside the cylinder, the magnetic field due to current through the a circular cylinder varies as

Liquid a has higher vapour pressure than liquid b. Which liquid out of a and b will have lower boiling point.

With respect to a rectangular Cartesian co-ordinate system three vectors are expressed as $\overrightarrow{a}=4\hat{i}-\hat{j},\overrightarrow{b}=-3\hat{i}+2\hat{j}$ and $\overrightarrow{c}=-\hat{k}$ where $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along the x, y and z axes respectively. The unit vector along the direction of sum of these vectors is

At what height $(h<<R)$ above the surface of Earth the value of $g$ decreases by $2\%?$ (radius of the Earth is $6400\text{km}$)

A satellite is launched in the equatorial plane is such a way that it can transmit signals up to ${60}^{\circ }$ latitude on the earth. Then the angular velocity of the satellite is

A wire stretched between two rigid supports vibrates in its
fundamental mode with a frequency of 45 Hz. The mass of the wire is
3.5 × 10^–2 kg and its linear mass density is
4.0 × 10^–2 kg m^–1. What is
(a) the speed of a transverse wave on the string, and (b) the tension
in the string?

If a particle is moving with velocity $v=y\hat{i}+2x\hat{j}$, then the locus of its path is

A uniform string of length $20m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (take $g=10m{s}^{-2}$)

Two plane mirrors are inclined at angle $\theta$ as shown in figure. If a ray parallel to $OB$ strikes the other mirror at $P$ and finally emerges parallel to $OA$ after two reflections, then $\theta$ is equal to

An impulsive force $\left(F\right)$ acts on a body which changes with time $\left(t\right)$. The $F-t$ graph is shown below. The value of impulse in time $\pi \text{sec}$ will be:

A $p-V$ diagra has been obtained from a test on a reciprocating compressor. Which of the following represents that diagram?