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The classroom door is of width $50\text{cm}$. The force of $5\text{N}$ is applied on the handle which is situated in the middle of the smaller plate as shown below. Compute the torque about the hinge (lever arm) of the door.

Calculate the energy in $\text{eV}$ of $1$ mole of photons having a wavelength of $331\text{nm}$.

The position vector $\overrightarrow{r}$ of a particle of mass $0.1\text{kg}$ is given by the equation $\overrightarrow{r}\left(t\right)=(\frac{10}{3}{t}^3\hat{i}+5t^2\hat{j})\text{m}$. At $t=1\text{s}$, the torque experienced by the particle due to force with respect to the origin is given by

Which of the following graphs represents the motion of the planet moving around the Sun.T is the

period of revolution and r is the average distance (from centre to centre) between the Sun and the

planet

A positively charged pendulum is oscillating in a uniform electric field pointing upwards. It's time period as compared to that when it oscillates without electric field is more How?

In given figure, pulley having radius, $r=1\text{m}$ and moment of inertia $I=2{\text{kgm}}^2$ about its axis of rotation. If $T_1=4\text{N}$ and $T_2=2\text{N}$ are the tension in the strings. Find the angular acceleration of pulley. (Take anti-clockwise rotation +ve)

In a gravitational field, at a point where the gravitational potential is zero

Three particles of masses 0.50 kg, 1.0 kg and 1.5 kg are placed at the three corners of a right-angles triangle of sides 3.0 cm, 4.0 cm and 5.0 cm as shown in figure. Locate the centre of mass of the system taking O as origin

A wire elongates by $1.0\text{mm}$ when a load $W$ is hanged from it. If this wire goes over a pulley, and two weights W each are hung at the two ends, the elongation of the wire will be

1. 1.81

A
person trying to lose weight (dieter) lifts a 10 kg mass, one
thousand times,
to
a height of 0.5 m each time. Assume that the potential energy lost
each time she lowers the mass is dissipated. (a) How much work does
she do against the gravitational force? (b) Fat supplies 3.8 ×
10⁷
J
of energy per kilogram which is converted to mechanical energy with a
20% efficiency rate. How much fat will the dieter use up?

If a light of intensity $60\text{W}$ falls normally on an area of $1{\text{m}}^2$. If the reflectivity of the surface is $75\%$, find the force experienced by the surface.

A simple pendulum with lenght $l$ and bob of mass $m$ is executing S.H.M. of small amplitude $a$. The maximum tension in the string will be

An unpolarised light is incident upon a glass plate of refractive index 1.54 at Brewster’s angle and gets completely plane polarized. The angle of polarization is: $(giventan{57}^{\circ }=1.54$)

A charge q, m enters a finite B - field with a speed v as shown (such that the charge enters the magnetic field region perpendicularly at a distance L from the top left corner in the figure). Find its deviation if $v=\frac{2qBL}{m}$

A body of mass m moving with a constant velocity v hits another body of the same mass moving with the same velocity v but in the opposite direction and sticks to it. The velocity of the compound body after collision is

Figure shows three concentric thin spherical shells $\text{A, B}$ and $\text{C}$ of radii $R,2R$ and $3R$. The shell $\text{B}$ is earthed and $\text{A}$ and $\text{C}$ are given charges $q$ and $2q$, respectively. Find the charges appearing on all the surfaces of $\text{A, B}$ and $\text{C}$.

The photoelectric thresshold wavelength of silver is $3250\times {10}^{-10}m$. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength $2536\times {10}^{-10}m$ is approximately
(Given $h=4.14\times {10}^{-15}eV$ and $c=3\times {10}^{8}m{s}^{-1}$)

A particle of mass 'm' is projected with velocity 'u' at an angle $\theta$ with horizontal. During the period when the particle descends from highest point to the position where its velocity vector makes an angle $\frac{\theta }{2}$ with horizontal, work done by the gravity force is

1. 15.8

A massless rod $BD$ is suspended by two identical massless strings $AB$ and $CD$ of equal lengths. A block of mass $m$ is suspended from point $P$ such that $BP$ is equal to $x$. If the fundamental frequency of the left wire is twice the fundamental frequency of right wire, then the value of $x$ is:

A racer drives his bike starting from rest on a circular track of radius $40\text{m}$ and having tangential acceleration of $3{\text{m/s}}^2$. What is the magnitude of net acceleration of the racer $5\text{s}$ after he starts to drive the bike?

What is the potential difference between the terminals of a battery if $250\text{J}$ of work is required to transfer $20\text{C}$ of charge from one terminal of the battery to the other?

A cyclist taking turn bends inwards while a car passenger taking same turn is thrown outwards. The reason is

The wavenumber of last line of Lyman series of hydrogen spectrum is $109674{\text{cm}}^{-1}$. The wave number of $H-\alpha$ line in Balmer series $H{e}^{+}$ is :

In the figure shown about what position does the block perform SHM?[K=10N/m, F= 100N]

In a Quincke's tube experiment, the sound intensity being detected at an appropriate point, changes from minimum to maximum for the second time, when the sliding tube is drawn out by $18.0\text{cm}.$ If the speed of sound in air is $340\text{m/s}$, then find the frequency of this sounding source.

In case of a compound microscope, an angular magnification of $30X$ is to be achieved using an eyepiece of focal length $5\text{cm}$ and an objective lens. Find the magnifying power of objective lens if the angular magnification is achieved in case of normal adjustment.

A liquid having mass $m=250\text{g}$ is kept warm in a vessel by using an electric heater. The liquid is maintained at ${50}^{\circ }\text{C}$ when the power supplied by the heater is $30\text{W}$ and the surrounding temperature is ${20}^{\circ }\text{C}$. As the heater is switched off, the liquid starts cooling and it was observed that it takes $10\text{sec}$ for temperature to fall from ${40}^{\circ }\text{C}$ to ${39.9}^{\circ }\text{C}$. Calculate the specific heat capacity of the liquid. Assume Newton's law of cooling to be applicable.

The equation of motion of a particle started at $t=0$ is given by $x=5$ sin $(20t+\frac{\pi }{3}),$ where x is in centimetre and t in second. When does the particle

(a) first come to rest

(b) first have zero acceleration

(c) first have maximum speed ?

A body is projected with an initial velocity of (5 $\hat{i}$ + 8 $\hat{j}$) m/s. The range of the projectile (g = 10 m / $s^2$)

The figure shows a color-coded resistor, the resistance of this resistor is

Consider two ideal diatomic gases $A$ and $B$ at some temperature $T$. Molecules of the gas $A$ are rigid, and have a mass $m$. Molecules of the gas $B$ have an additional vibrational mode, and have a mass $\frac{m}{4}$. The ratio of the specific heats $(C_V{)}_A$ and $(C_V{)}_B$ of the gases $A$ and $B$ respectively, is:

Two chrges $5\mu \text{C}$ and $4\mu \text{C}$ are separated by a distance $20\text{cm}$ in air work to be done to decrease the distance to $10\text{cm}$ is