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A uniform thin rod of length $l$ and mass $m$ is hinged at a distance $l/4$ from one of the end released from horizontal position as shown in figure. The angular velocity of the rod as it passes the vertical position is

Force required to pull a rectangular plate of length $2\text{cm}$ and breadth $3\text{cm}$ from water surface for which surface tension is $75\text{dyne/cm}$ is

A resistor $R$ and $2\mu F$ capacitor are connected in series through a $200V$ direct supply. Across the capacitor there
is a neon bulb that lights up at $120V$. Find the value of $R$ to make the neon bulb light up exactly $5s$ after the switch has been closed. (Take $lo{g}_{10}\left(2.5\right)=0.4$)

Consider the situation shown in figure. The switch $S$ is open for a long time and then closed. Find the charge flown through the battery when the switch is closed.

Effective capacitance between A & B is

A car is initially at rest at a distance of $330\text{m}$ from a stationary observer. It begins to move towards the observer with an acceleration of $1.1{\text{m/s}}^2$, sounding its horn continuously. $20\text{s}$ later the driver stops sounding the horn. The observer will hear the sound of horn for a duration of:

(Take velocity of sound in air to be $330\text{m/s})$

Two stars of masses $3\times {10}^{31}\text{kg}$ each and at distance $2\times {10}^{11}$ m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is :
(Take Gravitational constant )
$G=6.67\times {10}^{-11}N{m}^{2}K{g}^{-2})$

If $1\mu \text{F}$ capacitor holding a charge of $1\times {10}^{-5}\text{C}$ is connected to a $10\Omega$ resistor via a switch. What current will flow after the switch is closed?

A family went for a vacation. Unfortunately, it rained daily for $13$ days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all, they enjoyed $11$ mornings and $12$ afternoons. How many days in all did they stay there?

From a uniform square plate, one fourth part is removed as shown in figure. The centre of mass of remaining part will lie on line joining

A satellite can be in a geostationary orbit around the earth at a distance $r$ from the centre. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if its distance from the center is

The motion of a body is given by $\frac{dv}{dt}=6-3v$ where $v$ is the velocity (in $m{s}^{-1}$) at a time $t$ (in seconds). The body is at rest at t = 0. The terminal speed of the body is

The weight of a body at the centre of the earth is

At room temperature
(27.0 °C) the resistance of a heating element is 100 Ω.
What is the temperature of the element if the resistance is found to
be 117 Ω, given that the
temperature coefficient of the material of the resistor is

For what value of angle of incidence a ray incident on a glass plate $(\mu =1.5)$ will the reflected ray and the refracted ray be perpendicular to each other?

The 200 m free style women's swimming gold medal at Seol Olympic 1988 went to Heike Friendrich of East Germany when she set a new Olympic record of 1minute and 57.56 seconds. Assume that she covered most of the distance with a uniform speed. Calculate the average force of resistance offered by the water during the swim.

Two plates 1 and 2 move with velocities $v$ and $2v$ as shown. If the sphere does not slide relative to the plates and assuming the mass of each body as $m$, find the kinetic energy of the system (plates + sphere).

A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following

The earth receives solar radiation, at a rate of $8.2{\text{J cm}}^{-2}{\text{min}}^{-1}$. Assuming that the sun radiates like a blackbody, calculate the surface temperature of the sun. The angle subtended by the sun on the earth is ${0.53}^{\circ }$ and the Stefan's constant $\sigma =5.67\times {10}^{-8}$${\text{Wm}}^{-2}{\text{K}}^{-4}$ .

Identify the condition in which image formed is real, inverted and diminished from the following.

A luminous object is placed at a distance of $30\text{cm}$ from the convex lens of focal length $20\text{cm}$. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature $10\text{cm}$ be placed in order to have an upright image of the object coincident with it?

A
power transmission line feeds input power at 2300 V to a stepdown
transformer with its primary windings having 4000 turns. What should
be the number of turns in the secondary in order to get output power
at 230 V?

In the circuit shown in figure, $V_A-V_B=19\text{V}.$ What is the potential difference across the $3\mu \text{F}$ capacitor ?

A block of mass $m$ is at rest under the action of force $F$ against a wall as shown in figure. Which of the following statement is incorrect ?

A gas flushes out of a container through a pin hole four times quickly as methane. The molecular weight of the gas is

Silver has a work function of $4.7\text{eV}$. When ultraviolet light of wavelength $100\text{nm}$ is incident upon it, a potential of $7.7\text{V}$ is required to stop the photoelectrons from reaching the collector plate. How much potential will be required to stop the photoelectrons when light of wavelength $200\text{nm}$ is incident upon silver?

A steel bar of length L is fixed at the ends and is subjected to a non-uniform increase in temperature represented by the expression $T_x=T.\frac{x^3}{L^3}$ as shown in figure. Wha t is the value of compressive stress setup in the bar?

Obtain the equivalent emf and internal resistance of a parallel combination of 2 cell of emf E1 and E2 and internal resistance R1 and R2.

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