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A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $4 \text{ m s}^{-1}$. The ball strikes the water surface after $4 \text{ s}$. The height of bridge above water surface is: (Take $g=10 \text{ m s}^{-2}$)
The unit of Planck's constant is:
Two bodies of different masses $m_a$ and $m_b$ are dropped from two different heights $a$ and $b$. The ratio of the time taken by the two to cover these distances is:
A body dropped from a height $h$ with an initial speed of zero, strikes the ground with a velocity $3 \text{ km/h}$. Another body of the same mass is dropped from the same height $h$ with an initial speed $u' = 4 \text{ km/h}$. Find the final velocity of the second body with which it strikes the ground.
With what velocity a ball be projected vertically so that the distance covered by it in 5th second is twice the distance it covers in its 6th second ($g=10 \text{ m/s}^2$)?
Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. The process is:
A stone dropped from a building of height $h$ reaches the earth after $t$ seconds. From the same building, if two stones are thrown (one upwards and other downwards) with the same velocity $u$ and they reach the earth surface after $t_1$ and $t_2$ seconds respectively, then:
Sound waves travel at $350 \text{ m/s}$ through warm air and at $3500 \text{ m/s}$ through brass. The wavelength of a $700 \text{ Hz}$ acoustic wave as it enters brass from warm air:
A car accelerates from rest at a constant rate $\alpha$ for some time, after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed is $t$, then the maximum velocity acquired by the car is:
A train of $150 \text{ meter}$ length is going towards north direction at a speed of $10 \text{ m/s}$. A parrot flies at the speed of $5 \text{ m/s}$ towards south direction parallel to the railway track. The time taken by the parrot to cross the train is:
A current loop consists of two identical semicircular parts each of radius $R$, one lying in the $x-y$ plane, and the other in the $x-z$ plane. If the current in the loop is $i$, what will be the resultant magnetic field due to the two semicircular parts at their common centre?
A body is released from a great height and falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies, two seconds after the release of the second body is:
A particle is projected up with an initial velocity of $80\text{ ft/sec}$. The ball will be at a height of $96\text{ ft}$ from the ground after (Given $g=32\text{ ft/s}^2$):
A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the terminal voltage of the battery when the circuit is closed?
When a ball is thrown up vertically with velocity $v_0$, it reaches a maximum height of '$h$'. If one wishes to triple the maximum height then the ball should be thrown with velocity:
If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three seconds, the time of the travel is:
The magnetic force acting on a charged particle of charge $-2 \mu C$ in a magnetic field of $2 T$ acting in y-direction, when the particle velocity is $(2\hat{i} + 3\hat{j}) \times 10^6 \text{ ms}^{-1}$ is:
A train moving at a speed of $220 \text{ ms}^{-1}$ towards a stationary object, emits a sound of frequency $1000 \text{ Hz}$. Some of the sound reaching the object gets reflected back to the train as an echo. The frequency of the echo as detected by the driver of the train is (speed of sound in air is $330 \text{ ms}^{-1}$)
A closely wound solenoid of 2000 turns and area of cross-section $1.5 \times 10^{-4} \text{ m}^2$ carries a current of $2.0 \text{ A}$. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field $5 \times 10^{-2} \text{ T}$ making an angle of $30^{\circ}$ with the axis of the solenoid. The torque on the solenoid will be
The circuit is equivalent to: