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If a shell at rest explodes, then, the centre of mass of the fragments

What is slope in simple language and its types?

The vector $\overrightarrow{c}$, directed along the internal bisector of the angle between the vectors $\overrightarrow{a}=7\hat{i}-4\hat{j}-4\hat{k}$ and $\overrightarrow{b}=-2\hat{i}-\hat{j}+2\hat{k}$ with $|\overrightarrow{c}|=5\sqrt{6}$ is,

Prove the law of conservation of mechanical energy in a free fall.

A few electric field lines for a system of two charges $Q_1$ and $Q_2$ fixed at two different points on the $x-$ axis are shown in the figure. These line suggest that

A block is released from a height $h$ on a track $AB$ as shown in the figure. From $C$ there is a circular track of radius $R=50\text{cm}$.



Assuming all the surfaces to be smooth, the minimum value of $h$ for which the block reaches the point $D$ is

The particle moves in rectilinear motion as given in the acceleration – displacement $(a-s)$ curve shown in the figure. Determine the velocity after the particle has travelled $30\text{m}$, if the initial velocity is $10\text{m/s}$.

A $1.0kg$ block collides with a horizontal weightless spring of force constant $2.75N{m}^{–1}$ as shown in figure. The block compresses the spring $4.0m$ from the rest position. If the coefficient of kinetic friction between the block and horizontal surface is $0.25$, the speed of the block at the instant of collision is

A block of mass $0.1\text{kg}$ is held against a wall by applying a horizontal force of $5\text{N}$ on the block. If the coefficient of friction between the block and the wall is $0.5$, the magnitude of the frictional force acting on the block is

[Take $g=9.8{\text{m/s}}^2$]

For a prism, its refractive index is $\cot \frac{A}{2}$. Then the minimum angle of deviation is-

I received my favourite cologne, bottled in a metallic flask with a spherical cavity, on my birthday in December. I used it modestly only on special occasions, and found that I have finally emptied the bottle in mid-April, when the temperature had risen by ${25}^{\circ }C$ from December. If the metal's coefficient of superficial (area) expansion is $46\times {10}^{-5}{/}^{\circ }C$, how much extra cologne can I refill my bottle with, compared to the initial volume (answer in mL)?

When a $12\Omega$ resistor is connected with a moving coil galvanometer, then its deflection reduces from 50 divisions to 10 divisions. The resistance of the galvanometer is

1. 5

The given figure represents the phasor diagram of a series $LCR$ circuit connected to an $AC$ source. At instant $t$ when the source voltage is given by $V=V_0\cos \omega t$, the current in the circuit in terms of peak current $I_0$ will be

Given:

$V_{OR}=\sqrt{3}\text{V}$ = Voltage Across Resistor

$V_{OL}=3\text{V}$ = Voltage Across Inductor

$V_{OC}=2\text{V}$ = Voltage Across capacitor

Two satellites revolve around the sun, as shown in the figure. The first satellite revolves in a circular orbit of radius $R$ with speed $V_1$. The second satellite revolves in an elliptical orbit, for which minimum and maximum distances from the sun are $R/3$ and $5R/3$ respectively. Velocities of these positions are $V_2$ and $V_3$ respectively. The correct order of speeds is -

If a photocell is illuminated with a radiation of $1240{\text{A}}^{\circ }$, then stopping potential is found to be $8\text{V}$ . The work function of the emitter and the threshold wavelength are

Figure shows three containers. The rightmost container contains water (heat capacity $5cal{/}^{\circ }C$), initially at temperature ${100}^{\circ }\text{C}$. The middle container contains water maintained at ${80}^{\circ }\text{C}$ with the help of a heater. The container at the left hand side contains ice at $0^{\circ }\text{C}$. There are two heat conducting rods $A$ and $B$ both having thermal resistance equal to ${10}^{\circ }\text{C}\text{s/cal}$. Disregard any heat loss in the surrounding.





Find the rate with which ice melts in the leftmost container.

Which of the following curves between electric field $\left(E\right)$ at a distance $\left(x\right)$ from an infinite long uniformly charged sheet is correct?

[Assume $x$ to be very small as compared to dimension of sheet]

A particle moving along a circle has velocity $\overrightarrow{v}=2\hat{i}+3\hat{j}+5\hat{k}m/s$ and angular velocity $\overrightarrow{\omega }=2\hat{i}+2\hat{j}-2\hat{k}$, at a particular instant. The magnitude of centripetal acceleration of the particle is

A block of mass $2\text{kg}$ is placed on the floor. The coefficient of static friction is $0.4$. If a force of $2.8\text{N}$ is applied on the block parallel to the floor, the force of friction between the block and floor is (take $g=10{\text{ms}}^{-2}$)

For the given equation $\sqrt{2}{x}^2-3x+\sqrt{2}=0$, the value of roots are

A wedge of mass $M=4m$ lies on a frictionless plane. A particle of mass $m$ approaches the wedge with speed $v.$ There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by-

If $E_A,E_B,E_{C}and{E}_D$ represent the magnitudes of electric fields at A, B, C and D. Which of the options are correct?

In a space, potential $\left(V\right)$ is given by $V={\log }_e\left(xy\right)$, where $V,x,y$ are in SI units. The angle between $\overrightarrow{E}$ & $X$-axis at point $(6,6\sqrt{3})\text{m}$

If $\overrightarrow{A}=\hat{i}Acos\theta +\hat{j}Asin\theta$, then another vector $\overrightarrow{B}$ which is orthogonal to $\overrightarrow{A}$ can be expressed as:

A solid of density D is floating in a liquid of density d. If v is the volume of solid submerged in the liquid and V is the total volume of the solid, then v/V equals to