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If the force (F), length (L) and time (T) are assumed to be the fundamental units, then the dimensional formula of the mass will be

A small body of superdense material, whose mass is twice the mass of the Earth but whose size is very small compared to the size of the Earth, starts from rest at a height H R above the Earth’s surface, and reaches the Earth’s surface in time t. Then t is equal to

A stone tied to an inextensible string of length $1\text{m}$ is released from horizontal position. The stone is free to revolve in a vertical plane around the other end of the string. Find the angular speed of the stone when the string makes an angle $\theta ={30}^{\circ }$ with horizontal. Take $g=10{\text{m/s}}^2$.

An deal spring having force constant k is suspended from the rigid support and a block of mass Mis attached to its lower end. The mass is released from the natural length of the spring. Then the maximum extension in the spring is

A sphere of radius $1.00\text{cm}$ is placed in the path of a parallel beam of light of large aperture. The intensity of the light is $0.50{\text{W/cm}}^2.$ If the sphere partially absorbs $(\alpha =0.25)$ the radiation falling on it, find the force exerted by the light beam on the sphere.

If the length of a second's pendulum is increased thrice, what would be its time period?

A current is made of two components a dc component $i_1=3A$ and an ac component $i_2=4\sqrt{2}sin\omega tA$. The reading of hot wire ammeter due this current is

The half-life of ${}^{198}Au$ is 2.7 days. Calculate the decay constant.Take atomic weightof ${}^{198}Au$ to be 198 g $mo{l}^{-1}$

SI unit of permittivity $\left(ϵ\right)$ is….. (if Coulomb (C), Meter (m) and Force (N) are fundamental Quantities

Oxygen boils at $-{183}^{\circ }C$ . This temperature is approximately

A current of $1.0\text{A}$ is established in a tightly wound solenoid of radius $2\text{cm}$ having $1000\text{turns/meter}.$ Find the magnetic energy stored in each meter of the solenoid.

To mop-clean a floor, a cleaning machine presses a circular mop of radius $R$ vertically down with a total force $F$ and rotates it with a constant angular speed about its axis. If the force $F$ is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is $\mu$, the torque applied by the machine on the mop is

The time dependence of the position of a particle of mass $m=2\text{kg}$ is given by $r\left(t\right)=2t\hat{i}-3t^2\hat{j}\text{m}.$ Its angular momentum (in ${\text{kg m}}^2/\text{s}$), with respect to the origin, at time $t=2\text{s}$ is

A batsman deflects a ball by an angle of ${45}^{\circ }$ without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)

What is the path difference between two waves $1$ and $2$ shown below?

A body is thrown with the velocity $u$ at an angle $\theta$ with the horizontal. If the body remains in air for 6 seconds, the maximum height reached by the body will be

1. -6

The bike of a stunt driver can achieve a maximum instantaneous velocity of $40\text{m/s}$. He starts at the base of a vertical circular track and intends to complete the vertical circle. What is the maximum radius of the track to ensure the safety of the driver?

Lifetimes
of the molecules in the excited states are often measured by using
pulsed radiation source of duration nearly in the nano second range.
If the radiation source has the duration of 2 ns and the number of
photons emitted during the pulse source is 2.5 × 10¹⁵,
calculate the energy of the source.

Three capacitors of capacitance $6\mu F$ each are available. The minimum and maximum capacitance which may be obtained are

Hot water cools from ${60}^{\circ }\text{C}$ to ${50}^{\circ }\text{C}$ in the first $10\text{min}$ and to ${42}^{\circ }\text{C}$ in the next $10\text{min}$. The temperature of the surrounding is

For a finite line charge, find the electric field at the non-axial point $\text{P}$, perpendicular to axis of line charge.

Is it possible for an object to be travelling with a non-zero velocity if the object experiences a net zero external force?

A particle moves on a straight line and its a - t graph is shown.

List - I gives some quantites and List - II gives some possible magnitudes of quantites then correct match is



$\begin{array}{cc}\text{List - I}& \text{List - II}\\ \text{I) Average velocity of 4 sec}& \text{P) 0}\\ \text{II) Average acceleration of 4 sec}& \text{Q) 5}\\ \text{III) Displacement in 4 sec}& \text{R) 10}\\ \text{IV) Velocity at t = 4 sec}& \text{S) 20}\\ & \text{T) 40}\\ & \text{U) 50}\end{array}$

A positive charge is moving towards a person. The direction of magnetic field lines will be in:

A projectile is fired from the surface of the earth with a velocity of $5{\text{ms}}^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3{\text{ms}}^{-1}$ at the same angle follows a trajectory while is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in ${\text{ms}}^{-2}$) is:

(Given $g=9.8{\text{m/s}}^2$)

The displacement of a particle along x-axis is given by x = 4 + 6t + 5t². Its acceleration at t = 2s

Moment of inertia of the circulr disc about the axis shown in the diagram is:

Three concentric spherical shells have radii $a,b$ and $c$ $(a<b<c)$ and have surface charge densities $\sigma ,-\sigma \text{and}\sigma$ respectively. If $V_A,V_B\text{and}{V}_C$ denote the potentials of the three shells, then for $c=a+b$. We have

A motorcycle has to move with a constant speed on an overbridge which is in the form of a circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point. (a) What can its maximum velocity be for which the contact with the road is not broken at the highest point ? (b) If the motorcycle goes at speed $\frac{1}{\sqrt{2}}$ times the maximum found in part (a), where will it lose the contact with the road ? (c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge ?

Four spheres of mass $M$ and radius $R$ each are touching each other as shown. Calculate the MI about the axis which passes through centre of the square and perpendicular to the plane.