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A particle $A$ is projected with an initial velocity of $60\text{m/s}$ at an angle ${30}^{\circ }$ to the horizontal. At the same time a second particle $B$ is projected in opposite direction with initial speed of $50\text{m/s}$ from a point at a distance of $100\text{m}$ from $A$. If the particles collide in air find the angle of projection $\alpha$ for particle $B$

For diamond, if critical angle is ${30}^{\circ }$ (outside medium is air with $\mu =1$), then speed of light in diamond and wavelength of yellow colour in diamond (${\lambda }_{yellowinair}=600nm$) are respectively

A stone of mass $5\text{kg}$ is tied to a string of length $2.5\text{m}$, is whirled round in a horizontal circle. What is the maximum angular velocity with which the stone can be whirled around, if the string can withstand a maximum tension of $1250\text{N}$ ?

Two equal point charges are fixed at x=-a and x=+a on the x axis another point charge Q is placed at the origin . The change in the electrical potential energy of Q when it's displaced by a small distance x along the x axis is approximately proportional to ?

A bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb

A projectile is fired horizontally from a gun that is 45.0 m above flat ground, it emerges from the gun with a speed of 500 m/s. (take, g = $-10m/s^2$)

Column - I Column - II

(i) Time of flight of Projectile in s (x) 3

(ii) Horizontal distance covered by projectile in m (y) 30

(iii) Magnitude of vertical component of velocity in m/s as it strikes ground(z) 1500

I m so late so can i start MOTION IN ONE DIMENSION first by regarding UNITS AND DIMENSION....... .

A block of mass $m$ is attached with a massless spring of force constant $k$. The block is placed over a rough inclined surface for which the coefficient of friction is $\mu =\frac{3}{4}$. The minimum value of $M$ required to moved the block up the plane is (Neglect mass of pulley, string and friction in pulley).

Find the normal force and acceleration respectively of the $2\text{kg}$ block shown in the figure.
$\text{(Take}g=10{\text{m/s}}^2\text{)}$

The count rate from a radioactive sample fails from 4.0 $\times {10}^6$ per second to 1.0 $\times {10}^6$ per second in 20 hours. What will be the count rate 100 hours after the beginning ?

Angular momentum of body about a point $A$ is given as $\overrightarrow{L}=(4t^2+6)\hat{k}$. Find the net torque acting on body about point $A$ at $t=3\text{sec}$.

Frequency of photon having energy 66 eV is

A particle of mass 1 kg is placed at a distance of 4 m from the centre and on the axis of a uniform ring of mass 5 kg and radius 3m. What is the work required to be done to increase the distance of the particle from 4m to 3$\sqrt{3m}$

A body takes just twice the time as long to slide down a plane inclined at ${30}^o$ to the horizontal as if the plane were friction less. The coefficient of friction between the body and the plane is

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

Molar specific heat at constant volume $C_v$ for a monoatomic gas is

Two identical rods each of mass 'M' and length 'l' are joined in crossed position as shown in figure. The moment of inertia of this system about a bisector would be

A particle of mass m is attached to three identical springs A, B and C each of force constant k as shown in figure. If the particle of mass m is pushed slightly against the spring A and released, the time period of oscillation is:

$\sqrt{-2}$ $\sqrt{-3}$=

A charge of $3.14\times {10}^{-6C}$ is distributed uniformly over a circular ring of radius 20.0 cm. The ring rotates about its axis with an angular velocity of 60.0 rad $s^{-1}.$ Find the ratio of the electric field to the magnetic field at a point on the axis at a distance of 5.00 cm from the centre.

From a solid sphere of mass M and radius R, a cube of maximum possible volume is cut. The moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is

Give the benefits and limitations of using solar power.

Consider the situation of the previous problem. The man has to reach the other shore at the point, directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk down to this point. Find the minimum distance that he has to walk.

A point source S is placed midway between two converging mirrors having equal focal length f as shown in figure. Find the values of d for which only one image is formed.

A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite directions (figure 12-E16). The separation between the wheels is L. The friction coefficient between each wheel and the plate is $\mu .$ Find the time period of oscillation of the plate if it is slightly displaced along its length and released.

Consider the following very rough model of a beryllium atom. The nucleus has four protons and four neutrons confined to a small volume of radius ${10}^{-15}m.$ The two 1 s electrons make a spherical charge cloud at an average distance of $1.3\times {10}^{-11}m$ form the nucleus, whereas the two 2 s electrons make another spherical cloud at an average distance of $5.2\times {10}^{-11}m$ form the nucleus. Find he electric field at (a) a point just inside the 1 s cloud and (b) a point just inside the 2 s cloud.

The penetration of light into the region of geometrical shadow is caused due to______.

A force $10\text{N}$ acts tangentially at the highest point of a solid sphere of mass $10\text{kg}$ kept on a rough horizontal plane. If the sphere rolls without slipping, find the acceleration of the centre of the sphere (in $\text{m}/{\text{s}}^2$).

Find the force exerted by $3\text{kg}$ body on $1\text{kg}$ assuming all surfaces are smooth ($g=10{\text{m/s}}^2$)

A point charge of magnitude q = 4.5 nC is moving with speed v = $3.6\times {10}^7$ m/s parallel to the x-axis along the line y = 3 m. Find the magnetic field at the origin produced by this charge when the charge is at the point x = -4 m, y = 3 m, as shown in the figure.

A hydrogen atom moving at speed v collides with another hydrogen atom kept at rest. Find the minimum value of v for which one of the atoms may get ionized. The mass of a hyd rogen atom = $1.67\times {10}^{-27}$ kg

The $x-t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=\frac{4}{3}\text{s}$ is

A body is moved along a straight line by a machine delivering a constant power.How does the distance moved by the body depends on time.

How many NAND gates are used to form an AND gate

A wheel rotates with a constant angular acceleration of $3.6{\text{rad/s}}^2$. If angular velocity of the wheel is $4.0\text{rad/s}$ at time $t_0=0$, what angle does the wheel rotate in $1\text{s}$? What will be its angular velocity at $t=1\text{s}$?

Show that the minimum energy needed to separate a proton from a nucleus with Z protons and N neutrons is $△E=(M_{z-1,N}+M_H-M_{Z,n})C^2$ Where $M_{Z,n}$= mass of an atom with Z protons and N neutrons in the nucleus and $M_H$= mass of a hydrogen atom. This energy is known as proton-separation energy.

A source of sound of frequency 450 cycles/sec is moving towards a stationary observer with 34 m/sec speed. If the speed of sound is 340 m/sec, then the apparent frequency will be

A straight wire of length l can slide on two parallel plastic rails kept in a horizontal plane with a separation d. The coefficient of friction between the wire and the rails is $\mu$. If the wire carries a current i, what minimum magnetic field should exist in the space in order to slide the wire on the rails.

An electron is accelerated through a potential difference of $10,000V$. Its de Broglie wavelength is (nearly) $\left(m_e=9\times {10}^{-31}kg\right)$

A block of mass $m$ is connected to springs as shown in the figure. Find the time period of small oscillations.
[All springs are identical]

With what acceleration $\left(a\right)$ should the box in the figure descend so that the block of mass $M$ exerts a force $\frac{Mg}{4}$ on the floor of the box?

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration $\alpha$ to keep the block stationary. Then $\alpha$ is equal to

A parallel plate capacitor filled with air has a capacitance of $C$. The distance of separation between the plates is $d$ and the potential difference of $V$ is applied between the plates. Force of attraction between the plates of the parallel plate capacitor is