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A stone tied to a string is rotated with a uniform speed in a vertical plane. If mass of the stone is $m$, the length of the string is $r$ and the linear speed of the stone is $v$, when the stone is at its lowest point, then the tension in the string will be ($g=$ acceleration due to gravity)

Linear mass density of a bar is $\rho =\frac{{\rho }_o}{L_o}L+{\rho }_o$ where ${\rho }_o$ is constant and $L_o$ is length of bar. Its centre of mass from one of the end is
(Assume the other dimensions of the bar to be unity)

The greatest acceleration or deceleration that a train may have is ${}^{\prime }{a}^{\prime }$. The minimum time in which the train can get from one station to the next at a distance ${}^{\prime }{s}^{\prime }$ is –

What is the unit of specific latent heat.

What should be the maximum value of $M$ so that the $4\text{kg}$ block does not slip over the $5\text{kg}$ block: (Take $g=10{\text{m/s}}^2)$

Two blocks of masses $3\text{kg}$ and $2\text{kg}$ are tied to two ends of an inextensible string which passes over a frictionless pulley. The tension in the string between ceiling and the axle of pulley is

The electric flux $\left({\varphi }_E\right)$ in a space varies with time $\left(t\right)$ as, ${\varphi }_E=250t^2+100t-120$, where $t$ is in $\text{second}$. The magnitude of displacement current at $t=10\text{s}$ is -



Take ${ϵ}_0=8.85\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$

A nucleus with mass number $220$ initially at rest, emits an $\alpha$ -particle. If the $Q$ value of the reaction is $5.5MeV$, then the kinetic energy of the $\alpha$ -particle is

A transverse harmonic wave on a string is described by

Where x and y are in cm and t in s. The
positive direction of x is from left to right.

(a) Is this a travelling wave or a stationary wave?

If it is travelling, what are the speed and direction of its
propagation?

(b) What are its amplitude and frequency?

(c) What is the initial phase at the origin?

(d) What is the least distance between two successive crests in
the wave?

A bob attached to a light string of length $10\text{m}$ is given an initial velocity of $20\text{m/s}$ at the bottom-most point to perform vertical circular motion. What will be the velocity of bob just before slacking of string?

(Take $g=10m/s^2$)

The value of $\frac{4(cos{75}^{\circ }+isin{75}^{\circ })}{0.4(cos{30}^{\circ }+isin{30}^{\circ })}$ is

The radioactive decay of uranium into thorium is represented by the equation

${}_{92}^{238}U\to {}_{90}^{234}Th+x$

What is x?

Two wires of equal
length, one of aluminium and the other of copper have the same
resistance. Which of the two wires is lighter? Hence explain why
aluminium wires are preferred for overhead power cables. (ρ_Al
= 2.63 × 10⁻⁸ Ω m, ρ_Cu
= 1.72 × 10⁻⁸ Ω m, Relative density of
Al = 2.7, of Cu = 8.9.)

A long insulated copper wire is closely wound as a spiral of ${}^{\prime }{N}^{\prime }$ turns . The spiral has inner radius ${}^{\prime }{a}^{\prime }$ and outer radius ${}^{\prime }{b}^{\prime }$ .



The spiral lies in the $X-Y$ plane and a steady current ${}^{\prime }{I}^{\prime }$ flows through the wire . The Z-component of the magnetic field at the center of the spiral is

Choose the correct answer from among the given ones:

For the problem 8.10, the direction of the gravitational intensity at an arbitrary point P is indicated by the arrow (i) d, (ii) e, (iii) f, (iv) g.

A body starts from rest and moving with an acceleration of $1{\text{ms}}^{–2}$. The displacement of the body in $5$ seconds is

Find $|\overrightarrow{a}-\overrightarrow{b}|$, if two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are such that $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=3$ and $\overrightarrow{a}.\overrightarrow{b}=4$

A concave mirror of focal length 20 cm produces an image twice the height of the object.if the image is real,then distance of the object from the mirror is

1. 20cm.

2. 60cm.

3. 10cm.

4. 30cm

The bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of $\sqrt{3gl}$. Find the angle rotated by the string before it becomes slack.