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A slit of width $a$ is illuminated by white light. The first minima for red light $(\lambda =6500\mathring{\text{A}})$ will fall at $\theta ={30}^{\circ }$, when $a$ will be equal to,

A string can withstand a tension of $25\text{N}$. What is the greatest speed at which a body of mass $1\text{kg}$ can be whirled in a horizontal circle using a $1\text{m}$ length of a string ?

What is momentum and impulse ?

A point moves rectilinearly with deceleration which depends on the velocity $v$ of the particle as $a=k\sqrt{v}$, where $k$ is a positive constant. At the initial moment the velocity of the point is equal to $v_0$. What distance will it cover before it stops ?

A person is standing on a weighing machine placed on the floor of an elevator. The elevator starts going up with some acceleration, moves with uniform velocity for a while and finally decelerates to stop. The maximum and the minimum weights recorded are 72 kg and 60 kg. Assuming that the magnitudes of the acceleration and the deceleration are the same, find (a) the true weight of the person and (b) the magnitude of the acceleration. Take g = 9.9 $m/s^2$

An infinitely long thin non-conducting wire is parallel to the $z$ - axis and carries a uniform charge of line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ sustends an angle of ${120}^{\circ }$ at the centre $\text{O}$ of the spherical shell as shown in the figure. The electric flux through the shell is

A standing wave exists in a string of length 150 cm which is fixed at both ends with rigid supports. The displacement amplitude of a point at a distance of 10 cm from one of the ends is $5\sqrt{3}$ mm. The distance between the two nearest points, within the same loop and having displacement amplitude equal to $5\sqrt{3}$ mm is 10 cm. The maximum displacement amplitude of the particles in the string is

A particle moves in the $x-y$ plane and at time $t$, it is at the point whose coordinates are $(t^2,t^3-2t)$. Then at what instant of time will its velocity and acceleration vectors be perpendicular to each other?

A bullet moving with speed $100\text{m/s}$ strikes a block and get embedded into it. If mass of the block is nine times that of the bullet, find the impulse imparted by the bullet to the block (in $\text{Ns}$), given mass of the bullet is $m\text{kg}$.

A box $B$ of mass $M$ hangs from an ideal spring of force constant $k$. A small particle $A$ also of mass $M$ is stuck to the ceiling of the box and the system is in equilibrium. The particle gets detached from the ceiling and falls to strike the floor of the box. It takes time $t$ for the particle to hit the floor after it gets detached from the ceiling. The particle on hitting the floor sticks to it and the system thereafter oscillates with a time period of $T$. Find the height $H$ of the box if it is given that $t=\frac{T}{6}$. Assume that the floor and ceiling of the box always remain horizontal.

Two unknown resistances X and Y are connected in left and right gaps of a metre bridge and the balancing point is obtained at 50 cm from left. When a $20\Omega$ resistance is connected in series with X, the balancing point is at 60 cm from left. The values of X and Y respectively (in ohms) are

Why does the moon appear to move with same velocity as of car or us??

The numerical ratio of velocity to speed is:

More than One Answer Type

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A charged particle having charge q and mass m is moved in a space where a uniform electric field exists. If work done in moving the charge along the line y = x is zero, then which of the following may represent the electric field?



q आवेश व m द्रव्यमान वाले एक आवेशित कण को उस त्रिविम में गति करायी जाती है जहाँ एकसमान विद्युत क्षेत्र उपस्थित है। यदि आवेश को रेखा y = x के अनुदिश गति कराने में किया गया कार्य शून्य है, तब निम्नलिखित में से कौनसा विद्युत क्षेत्र को प्रदर्शित कर सकता है?

If ${\delta }_1$ and ${\delta }_2$ be the angles of dip observed in two vertical planes at right angles to each other and $\delta$ be the true angle of dip, then

The force with which the earth attracts an object is called the weight of the object. Calculate the weight of the moon from the following data : The universal constant of gravitation $G=6.67\times {10}^{-11}N-m{}^2/k{g}^2,$ mass of the moon = $7.36\times {10}^{22}kg,$ mass of the earth $=6\times {10}^{24}kg$ and the distance between the earth and the moon $=3,8\times {10}^{5}km.$

Statement-I: If a red color light gets refracted; it will still remain red in color after refraction.
Statement-II: Color depens on frequency, on refraction, the wavelength of the light changes.

If $\overrightarrow{E}$ and $\overrightarrow{B}$ are the electric and magnetic field vectors of E.M. waves then the direction of propagation of E.M. wave is along the direction of

Threshold wavelength for photoelectric effect on sodium is 5000 $\stackrel{\circ }{A}$. Its work function is

Two ice cubes are
pressed over each other and unite to form one cube. Which force is responsible
for holding them together?

A prism having refractive index 1.414 and refracting angle ${30}^{\circ }$ has one of the refracting surfaces silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is:

To a man running at the rate of $4\text{km/h}$, the rain appears to fall vertically. When he increases his speed to $8\text{km/h}$, rain appears coming to man at an angle of ${45}^{\circ }$ with vertical. Find the magnitude of velocity of rain with respect to ground.

The acceleration of a particle is increasing linearly with time t as bt . The particle starts from the origin with an initial velocity $v_o$. The distance travelled by the particle in time t will be

A wave is represented by the equation $y=7sin(7\pi t-0.04\pi x+\frac{\pi }{3})$ x is in metres and t is in seconds. The speed of the wave is

The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is

"The tip of second hand" of the clock takes $60\text{s}$ to move once on the circular dial of the clock. If the length of the second hand is $10\text{cm}$, calculate the speed of the tip of the second hand clock ?



$(\pi =22/7)$

A uniform ${}^{\prime }{T}^{\prime }$ shaped object with dimensions as shown in the figure, is lying on a smooth floor. A force $\overrightarrow{F}$ is applied at the point P parallel to limb $AB$, such that the object has only the translational motion without rotation. Find the distance of point $P$ from $C$

If force, $F=48N$ is acting on the system as shown in figure, find the tension in string. All surfaces are smooth.
(Take $g=10m/s^2$)

A cubical block of wood weighing 200 g has a lead piece fastened underneath. Find the mass of the lead piece which will just allow the block to float in water. Specific gravity of wood is 0.8 and that of lead is 11.3.

A particle of mass $1\text{kg}$ is moving in a circle of radius $0.36\text{m}$ such that its projection on diameter executes SHM. In $0.1\text{sec}$ interval, particle undergoes angular displacement of ${30}^{\circ }$. Find the force acting on particle at position $B$ if it starts from $A$.