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Find the acceleration of a system consisting of a cylinder of mass $m$ and radius $R$ and a plank of mass $M$ placed on a smooth surface if it is pulled with a force $F$ as shown in the figure. Given that sufficient friction is present between the cylinder and the plank surface to prevent sliding of the cylinder.

The electrostatic force
on a small sphere of charge 0.4 μC
due to another small sphere of charge − 0.8 μC
in air is 0.2 N. (a) What is the distance between the two spheres?
(b) What is the force on the second sphere due to the first?

What particle is produced when Plutonium-242 decays to Uranium-238?

A circular wire loop of radius $R$, mass $m$, and current $I$ lies on a rough surface. There is a horizontal magnetic field $\overrightarrow{B}$. The minimum value of current $I$ for which one edge of the loop will lift off the surface ?

A particle of mass $m$ and charge $q$ is placed at rest in uniform electric field $E$ and then released. The kinetic energy gained by the particle after a distance $y$ is

Two springs of equal lengths and equal cross-sectional areas are made of materials whose Young's moduli are in the ratio of 3:2. They are suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of

Assuming that the surface is frictionless and strings are inextensible, find the acceleration of the block of mass $2m$ shown in the figure.

The correct order of the decreasing ionic radii among the following isoelectronic species is

Find the angle between the net acceleration vector and tangential acceleration vector for a particle moving in a circle of radius $4m$ with its speed increasing at $3m/s$ every second, when the speed of the particle is $4m/s$.

Force acting on charges separated by some distance is shown in the figure.





Select the correct relation between given parameters :

The optical axes of a convex and concave lens are separated by a distance $5\text{mm}$ as shown in the figure. Find the coordinate of the final image formed by the combination if a parallel beam of light is incident on the convex lens. Origin is at the optical centre of the convex lens.

Can normal force do a nonzero work on an object.

A point charge $Q$ is located on the axis of a disc of radius $R$ at a distance $b$ from the plane of the disc. If one-fourth of the total electric flux from the charge passes through the disc, then choose the correct option.

In the circuit shown, initially $C_1$ and $C_2$ are uncharged. After closing the switch,

In the circuit shown, the current in $3\Omega$ resistance is

A particle covers 50 m distance when projected with an initial speed. On the same surface it will cover a distance, when projected with double the initial speed

Two coherent sources of light $S_1\text{and}{S}_2$, equidistant from the origin, are separated by a distance $2\lambda$ as shown. They emit light of wavelength $\lambda$. Interference is observed on a screen placed along a large circle of radius $R$. A point on the circumference is found to be a point of constructive interference. Then angle $\theta$ (in the first quadrant of the circle) is,

(Consider that the vertical diameter is the point where central bright fringe lies)

Two charges $Q$ & $-Q$ are kept at some distance, electric field at mid point is $\overrightarrow{E}$, find force on $Q$. (charges are isolated)

In the arrangement shown in the figure, mass of the block $A$ is $4$ times that of block $B$. The height $h=20\text{cm}$. At a certain instant, the block $A$ is released and the system is set in motion. What is the maximum height (in $\text{cm})$ that the body $B$ will go up? Assume enough space allowed for $B$ and $A$ (i.e $A$ and $B$ are of small size) and take $g=10{\text{m/s}}^2$

What
is the excess pressure inside a bubble of soap solution of radius
5.00 mm, given that the surface tension of soap solution at the
temperature (20 °C) is 2.50 × 10^–2
N m^–1?
If an air bubble of the same dimension were formed at depth of 40.0
cm inside a container containing the soap solution (of relative
density 1.20), what would be the pressure inside the bubble? (1
atmospheric pressure is 1.01 × 10⁵
Pa).

A particle is moving along positive $x-$axis with velocity

$v=A-Bt$ (where $A$ and $B$ are $+\text{ve}$ constants). Find the total distance travelled by the particle during $t=0$ to $t=3A/B$, if the particle is at origin at $t=0$. All the quantities are in $S.I$ units.

Two particles A and B are projected simultaneously with velocities $V_A=11\text{m/s}$ and $V_B=15\text{m/s}$ as shown in the figure. Find the time (in seconds) when they collide.

The effective capacitance of the network between terminals is

$($Given, $C=6\mu \text{F})$

If $\gamma$ denotes the ratio of two specific heats of a gas, the ratio of slopes of adiabatic and isothermal PV curves at their point of intersection is

A thin equiconvex lens is made of glass of R.I 1.5 and its focal length is 0.2 If it acts a concave lens of 0.5 m focal length when dipped in a liquid, the R.I of liquid is

1. 2200

A solid sphere of mass $M$ and radius $R$ is rolling without slipping as shown in figure. Find out the magnitude of total angular momentum of the sphere about point of contact $\left(P\right)$.

A uniform ring of mass $m$ and radius $a$ is placed directly above a uniform sphere of mass $M$ and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance $a\sqrt{3}$ as shows in the figure. The gravitational force exerted by the sphere on the ring will be

Co-efficient of friction between $5\text{kg}$ and $10\text{kg}$ blocks is $0.5$. If friction between them is $20\text{N}$. What is the value of force being applied on $5\text{kg}$. Assume the floor is friction less.

An electric motor creates a tension of 4500 N in a hoisting cable and reels it in at the rate of 2 m/s. What is the power of the electric motor?

Two identical sources each of intensity $I_0$ have a separation $d=\frac{\lambda }{8}$, where $\lambda$ is the wavelength of the waves emitted by either source. The phase difference of the sources is $\frac{\pi }{4}$. The intensity distribution $I\left(\theta \right)$ in the radiation field as a function of $\theta$, which specifies the direction from the sources to the distant observation point $P$ is given by