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Two-point charges of 2 micro C but opposite in sign are placed 10 cm apart to calculate the electric field at a. Point 10 cm from mid point on the axial line of dipole.

A block of mass 200 g is suspended through a vertical spring.The spring is stretched by 1.0 cm when the block is in equilibrium.A particle of mass 120 g is dropped on the block from a height of 45 cm.The particle sticks to the block after the impact.Find the maximum extension of the spring.Take g=10 $m/s^2$.

Two billiard balls each of mass 0.05 kg moving in opposite directions with speed $6m{s}^{-1}$ collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?

Find the force exerted by the water on a 2 $m^2$ plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface ?

1. 28.8

Which of the following represents the correct dimensions of the gravitational constant?

The alphabet $\text{S}$ is placed in front of a plane mirror.





Which of the following options correctly represents the image in the mirror?

A student measuring the diameter of a pencil of circular cross - section with the help of a vernier scale records the following four readings $5.50\text{mm},$ $5.55\text{mm,}$$5.45\text{mm},5.65\text{mm}.$ The average of these four reading is $5.5375\text{mm}$ and the standard deviation of the data is $0.07395\text{mm}.$ The average diameter of the pencil should therefore be recorded as :

A large open tank has two holes in the wall. One is a square hole of side $2\text{cm}$ at a depth of $5\text{cm}$ from the top and the other is a circular hole of radius $R$ at a depth of $20\text{cm}$ from the top. When the tank is completely filled with water, the quantity of water flowing out per second from both the holes is same. Then, what is the value of $R$?

Let v and a denote the velocity and acceleration respectively of a body in one dimensional motion.Then which of the statements are correct?

A) speed must decrease when a<0

B)speed must increase when a>0

C)speed will increase when both v and a are less than zero

D)speed will decrease when v<0 and a>0

It is a multi correct question

Water stored in a dam possesses ___.

Two points on string are being observed as a travelling wave passes them. The points are at $x_1=0$ and $x_2=1m$, the transverse motions of two points are found to be as follows $y_1=Asin(3\pi t+\frac{\pi }{8})$ and $y_2=Asin\left(3\pi t\right)$ t is in seconds and y in metre. Mark correct options

Find the time period of the spring mass system shown in the figure below.

A book of mass 5 kg is placed on a table and it is pressed by 10 N force then, normal force exerted by the table on the book is?

A pump is required to lift 1000 kg of water per minute from a well 20 m deep and eject it at a rate of 20 m/s.

(x) How much work is done in ejecting water?

(y) How much work is done in lifting water?

(z) What HP (horse power) engine is required for the purpose of lifting water?

(1) 2 $\times$${10}^5$ $\frac{j}{min}$ (2) 4 $\times$${10}^5$ $\frac{j}{min}$ (3) 3 $\times$${10}^5$ $\frac{j}{min}$

(4) 6.6 $\times$${10}^3$ $\frac{j}{s}$ (5) 8 $\times$${10}^4$ watts (6)${10}^5$ watts

Take g = $\frac{10m}{s^2}$

A straight rod length L(t), hinged at one end freely extensible at the other end, rotates through an angle $\theta$(t) about the hinge. At time t, L(t)=1 m, $\dot{L}\left(t\right)=1\frac{m}{s},\theta \left(t\right)=\frac{\pi }{4}rad\text{and}\dot{\theta }\left(t\right)=1\frac{rad}{s}$. The magnitude of the velocity at the other end of the rod is

In the LC circuit shown below, $C=1\mu \text{F}$. When the capacitor is fully charged up to $100\text{V}$, the switch $S$ is closed at $t=0$. The current in the circuit oscillates at a frequency of ${10}^3\text{Hz}$. The value of $L$ will be approximately equal to







Take ${\pi }^2\approx 10$

A block of mass of $m$ is projected along the surface of a smooth circular wall with velocity $v$. What is the value of average normal force exerted by the circular wall on the block during its motion from $A$ to $B$. Assume uniform speed during the journey.

Three concentric metallic spherical shells of radii $R,2R,3R$ are given charges $Q_1,Q_2,Q_3$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells $Q_1:Q_2:Q_3$ is

A manometer connected to a closed tap reads $3.5\times {10}^5{\text{N/m}}^2$. When the valve is opened, the reading of the manometer falls to $3.0\times {10}^5{\text{N/m}}^2$. Then, the velocity of flow of water is:-

A 3.0 cm wire carrying
a current of 10 A is placed inside a solenoid perpendicular to its
axis. The magnetic field inside the solenoid is given to be 0.27 T.
What is the magnetic force on the wire?

A container filled with liquid upto height h is placed on a smooth horizontal surface. Container is having a small hole at the bottom. As the liquid comes out from the hole, the container moves in a backward direction with acceleration 'a' and finally, when all the liquid is drained out acquires a velocity $v$ . Neglect mass of container. In this case -

A solid sphere is set into motion on a rough horizontal surface with a linear speed v in the forward direction and an angular speed v/R in the anticlockwise direction as shown in figure (10-E16). Find the linear speed of the sphere (a) when it stops rotating and (b) when slipping finally ceases and pure rolling starts.

When a mass of 8 kg is suspended from a string, its length is $l_1$. If a mass 10 kg is suspended, its length is $l_2$. Length, when a mass of 16 Kg is suspended from it, is given by

If $2000\alpha -$particles scattered at an angle of ${90}^{\circ }$ targeted at an atom, then the number of $\alpha -$particles scattering at ${60}^{\circ }$ will be -

Two equal masses (m) are projected at the same angle $\left(\theta \right)$ from two points separated by their range with equal velocities (v). The total momentum at the point of their collision is