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There are two horns $H_1$ and $H_2$ on a car. When sounded together, the driver records $35$ beats in $10$ seconds. With horn $H_2$ blowing and car moving towards a wall at a speed of $5{\text{ms}}^{-1}$, the driver noticed a beat frequency of $5\text{Hz}$ with the echo. When frequency of $H_1$ is decreased, the beat frequency with two horns sounded together increases. Calculate the frequencies of the two horns $H_1$ and $H_2$ respectively.



[Speed of sound = $332{\text{ms}}^{-1}$]

An electric dipole is placed at an angle of 30° with an electric field intensity of 2 × ${10}^5$ N/C. It experiences a torque equal of 4 Nm. The charge on the dipole, if the dipole length is 2 cm, is

A thin uniform disc of mass $M$ and radius $R$ has concentric hole of radius $r$. Find the moment of inertia of the disc about an axis passing through its centre and perpendicular to its plane.

A
14.5 kg mass, fastened to the end of a steel wire of unstretched
length 1.0 m, is whirled in a vertical circle with an angular
velocity of 2 rev/s at the bottom of the circle. The cross-sectional
area of the wire is 0.065 cm².
Calculate the elongation of the wire when the mass is at the lowest
point of its path.

A particle is projected with a velocity of 20 m/s at an angle of ${30}^{\circ }$ to an inclined plane of inclination ${30}^{\circ }$ to the horizontal. The particle hits the inclined plane at an angle ${30}^{\circ }$, during its journey. The time of flight in seconds is -

Ball $A$ having initial velocity $u=5\text{m/s}$ collides elastically with block $B$ initially at rest as shown in the figure. If both balls have the same mass, and the height of the tower is $h=20\text{m}$, find the horizontal distance $d$ traveled by ball $B$ before hitting the ground.

A force $\overrightarrow{F}=(a\hat{i}+b\hat{j})N$ acts on a body which displaces it by $\overrightarrow{s}=(c\hat{i}+d\hat{j})\text{m}$. The work done by the force is

A spherical ball of radius $r$ initially at rest on a rough horizontal surface is hit horizontally at a distance $x$ above the central line. Due to this sharp impulse the centre of ball acquires a velocity $v_c$. After some time, the ball will start pure rolling with a velocity equal to

Of the following sets of concurrent forces, the one which may be in equilibrium is

If two bodies were rubbed against each other and one aquired a -5mC charge, what will be the charge on the other body?

The position of the particle is given by $x=2t^2-4t+4$ in $\text{m}$. The average speed of the particle in $6\text{sec}$ is

A body is projected with a velocity of $30\text{m/s}$ at an angle of ${60}^{\circ }$ to the horizontal. Find the magnitude of velocity when the angle between the velocity vector and acceleration vector is ${120}^{\circ }$.

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 $mm$ of mercury. If the density of mercury is $13.6\times {10}^{3}kg/m^3$ and $g=10m/s^2$ , then the power of heart in Watts is

A ball is in a hot air balloon that starts from rest at t = 0 and accelerates upwards at 2m/s². After 10s, the ball is dropped from the balloon.Draw ball's v - t graph:

The load assembly as shown in figure mass of loadcell-1 is 100kg and loadcell-2 is 90 kg. Acceleration due to gravity is $9.8m/se{c}^2$ and Young's modulus is $1\times {10}^{11}N/m^2$. If area $\left(2c{m}^2\right)$ of load cells are same then amount of strain produced in load cell -1 and loadcell-2 respectively

An ideal transformer has $500$ primary turns and $10$ secondary turns. The primary coil carries current $2A$ and its voltage is $11,000V$. Current and voltage in the secondary coil will be

The friction coefficient between the two blocks shown in figure (6-E9) is $\mu$ but the floor is smooth.
(a) What maximum horizontal force F can be applied without disturbing the equilibrium of the system?
(b) Suppose the horizontal force applied is double of that found in Part (a). Find the accelerations of the two masses.

A cylindrical block of wood floats vertically with $80\%$ of its volume immersed in a liquid at $0^{\circ }\text{C}$. When the temperature of the liquid is raised to ${62.5}^{\circ }\text{C}$, the block just sinks in the liquid. The coefficient of cubical expansion of the liquid is

A block suspended from a vertical spring is in equilibrium. Show that the extension of the spring equals the length of an equivalent simple pendulum, i.e., a pendulum having frequency same as that of the block.

An inductor of inductance $20mH$, a capacitor of capacitance $100\mu F$ and a resistor of resistance $50\Omega$ are connected in series across a source of emf, $V=10\sin \left(314t\right)$. The power loss in the circuit is

Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in figure. Consider an axis $X{X}^{\prime }$, which is touching two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about $X{X}^{\prime }$ axis is :

A body of mass $400\text{g}$ slides on a rough horizontal surface. If the frictional force is $3.0\text{N}$, find the angle made by the contact force on the body with the vertical. Take $g=10{\text{m/s}}^2$

Transverse waves are generated in two uniform wires $A$ and $B$ of the same material by attaching their free ends to a vibrating source of frequency $200\text{Hz}$. The cross-sectional area of $A$ is half that of $B$ while the tension on $A$ is twice that on $B$. The ratio of the wavelengths of the transverse waves in $A$ and $B$ is

An inductor $(L=200\text{mH})$ is connected to an AC source of peak emf $210\text{V}$ and frequency $50\text{Hz}$. The value of peak current and instantaneous voltage of the source when the current is at its peak value is respectively :

Browsing through Mr. Fox's old scientific notes, Bruce Wayne encounters a secret temperature scale, which Mr. Fox called Z, in order to keep the Bat mobile's technology a secret. On that scale, the freezing and the boiling points of water were recorded to be -7⁰Z and 78⁰Z, respectively. The records instruct to maintain the coolant temperature at -24⁰Z for top speed. Mr. Wayne, naturally comfortable with the Fahrenheit scale due to his American upbringing, needs to calculate the coolant temperature in ⁰F. Help him choose the correct value

Consider the region formed by the lines $x=0,y=$ $0,x=2,y=2$. Area enclosed by the curves $y=e^x$ and $y=\ln x$, within this region is removed, then the area of the remaining region is: