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A stone is dropped into a lake from a tower 500 metre high. Taking the speed of sound as 330 m/s, the sound of the splash will be heard by the man approximately after

30 people gather in a $10\text{m}\times 5\text{m}\times 3\text{m}$ room for a confidential meeting. The room is completely sealed off and insulated. Calculate the rise in temperature of the room in half an hour. Assume that the average energy thrown off by the body of a person is $2500\text{kcal/day}$, density of air is $1.2{\text{kg/m}}^3$ and specific heat capacity of air at constant volume is $0.24\text{kcal kg}{{}^{-1}}^{\circ }{\text{C}}^{-1}$.
[Neglect volume occupied by the people].

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Why the net charge in a positive charged shell is zero ?

At what temperature will the speed of sound in hydrogen be the same as in oxygen at ${100}^0$ C? Molar masses of oxygen and hydrogen are in the ratio 16:1.

If the earth's magnetic field has a magnitude $3.4\times {10}^{-5}$ T at the magnetic equator of the earth, what would be its value at the earth's geomagnetic poles ?

In a nuclear fission reaction, a nucleus $A$ is divided into nuclei $B$ and $C$, their binding energies being $E_a$, $E_b$ and $E_c$ respectively. Then,

Three blocks of masses $m_1$, $m_2$ and $m_3$ are connected by massless strings as shown in the figure and placed on a frictionless table. A force of $40N$ pulls the system. Then calculate the value of $T$ (in $N$) if $m_1=10kg,m_2=6kg$ and $m_3=4kg$.

Find the radius of curvature of the simple microscope's lens whose maximum magnifying power is $6$. (Refractive index of glass used, ${\mu }_l=1.5)$

A ball is thrown upwards from the bottom of a fixed chamber of height $20\text{m}$ with a speed of $10\text{m/s}$. The interior of the chamber has no gravity. The ball strikes the ceiling of the chamber and rebounds. After $6\text{seconds}$, gravity is reintroduced in the chamber. The movement of the ball gradually slows down over time and the ball comes to rest. Which of the following is the correct displacement vs time graph for the movement of the ball inside the chamber?

Which chapter I do I first Introduction to 3D or straight line?

A particle moves under the effect of a force $F=k{x}^2$. Find work done by force when particle displaces from $x=0\text{m}$ to $x=4\text{m}$.

A particle is performing simple harmonic motion along $x-$ axis with amplitude $4\text{cm}$ and time period $1.2\text{sec}$. The minimum time taken by the particle to move from $x=+2\text{cm}$ to $x=+4\text{cm}$ and back again is given by

A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of heat insulator, and the piston is insulated by having a pile of sand on it/ by what factor does the pressure of the gas increase, if the gas is compressed to half it original volume?

An object is dropped from a height of $20\text{m}$. If a plane mirror is lying on the floor with the reflecting surface facing the object. The speed of image of the ball with respect to the ball just before striking the mirror will be

$($Take $g=10{\text{m/s}}^2)$

Find the minimum value of a function $y$, represented as $y=x^3-3x^2+6$.

If $x=asin[\omega t+\frac{\pi }{6}]and{x}^{\prime }=acos\omega t$, then what is the phase difference between the two waves?

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{dM\left(t\right)}{dt}=b{v}^2\left(t\right)$, where $v\left(t\right)$ is its instantaneous velocity. The instantaneous acceleration of the satellite is

An air cored toroid $10$ turns per $\text{cm}$ carries a current of $1\text{mA}.$ The intensity of magnetic field inside it is

Explain how you should catch a ball with newtons 2nd law

A body of mass m rises to a height h = R/5 from the earth's surface where R is earth's radius. If g is acceleration due to gravity , the increase in PE is

If focal length of an objective and eyepiece of a telescope are $3cm$ and $6cm$ respectively. The object (tiny) is placed at $2cm$ from objective and final image is formed at infinity, then the magnifying power of microscope is

Find the magnetic field B at the center of a rectangular loop of length l and width b,carrying a current i.

In the circuit diagram shown, $X_C=100\Omega ,X_L=200\Omega$ & $R=100\Omega$. The effective current through the source is

A long solenoid of $100\text{cm}$ length having $100$ turns, carries a current of $5\text{A}$. The magnetic field at the end of the solenoid is : $({\mu }_0=4\pi \times {10}^{-7}{\text{T m A}}^{-1})$

An insect moves in a circular path of radius $\frac{20}{\pi }\text{cm}$ steadily, and completes 25 revolutions in $100\text{s}$. What is the average angular speed and the average linear speed of the motion ?

A circular current carrying loop is placed in y-z plane such that its equation is given by y² + z² = 9 (here y and z are in cm). If current flowing in the loop is 5 A, then magnetic field at point (4 cm, 0, 0) will be



एक वृत्तीय धारावाही लूप को y-z तल में इस प्रकार रखा जाता है कि इसकी समीकरण को y² + z² = 9 (यहाँ y व z, cm में हैं) द्वारा व्यक्त किया जाता है। यदि लूप में प्रवाहित धारा 5 A है, तब बिंदु (4 cm, 0, 0) पर चुम्बकीय क्षेत्र होगा

If the ratio of magnetic fields at two points in a definite direction due to a long current carrying wire is $\frac{3}{4},$ then the ratio of the distances of these points from the wire will be :

A charged particle is fired at an angle $\theta$ to a uniform magnetic field directed along the $x–$axis. During its motion along a helical path, if the pitch of the helical path is equal to the maximum distance of the particle from the $x–$ axis, then

A soap film of thickness $0.0011\text{mm}$ appears dark when seen by the reflected light of wavelength $580\text{nm}$. What is the index of refraction of the soap solution, if it is known to be between $1.2$ and $1.5?$

The two rails of a railway track, insulated from each other and from the ground, are connected to a millivolt meter. What will be the reading of the millivolt meter when a train travels on the track at a speed of $180{\text{km h}}^{-1}$ ? The vertical component of earth's magnetic field is $0.2\times {10}^{-4}\text{T}$ and the rails are separated by $1\text{m}$.