Explore topic-wise InterviewSolutions in .

A projectile is given an initial velocity of $(\hat{i}+2\hat{j})\text{m/s}$. Then, the equation of its trajectory is: [Take $g=10{\text{m/s}}^2$]

A force is acting on a body of mass $3kg$ kept on a rough horizontal surface. If a friction force of $40N$ is required to keep the body at rest under the action of this external force. Find the contact force acting on the body. (Take $g=10m/s^2$)

In a head on elastic collision of a heavy vehicle moving with a velocity of $10{\text{ms}}^{-1}$ and a small stone at rest, the stone will fly away with a velocity equal to

Light of wavelengths $\lambda$ is incident on a slit of width d. The resulting diffraction pattern is observed on a screen at a distance D. The linear width of the principal maximum is equal to the width of the slit if D equals

A uniform rod of mass '$m$' and Length '$L$' is rotated about its perpendicular bisector at an angular speed $\omega$. Calculate its angular momentum about its Axis of rotation?

A radio receiver antenna that is 2 m long is oriented along the direction of the electromagnetic wave and receives a signal of intensity $5\times {10}^{-16}W/m^2$. The maximum instantaneous potential difference across the two ends of the antenna is

A particle executes simple harmonic oscillation with an amplitude $A$. If the time period of oscillation is $T$, then minimum time taken by the particle to travel half of the amplitude from the mean position is

According to a stationary observer on ground, a point object $O$ in front of a plane mirror $M$ and the mirror both are moving at $10\text{cm/s}$ and $20\text{cm/s}$ respectively towards right. Find the speed of the image as measured by the stationary observer.

If $\omega =1,$ the value of impedance of the given circuit is

A particle is initially at rest, moves along in a circle of radius $R=2\text{m}$ with an angular acceleration $\alpha =\frac{\pi }{8}{\text{rad/sec}}^2$. The magnitude of average velocity of the particle over the time it moves by half of the circle is

Two bodies of masses $100kgand10000kg$ are separated by distance of $1m$. The distance from the smaller body where the intensity of gravitational field is zero is

In the figure shown, the $12kg$ body pulled by a string with an acceleration $a=2.2m/s^2$. The tension $T_1$ and $T_2$ will be respectively

(Take $g=9.8m/s^2$)

If the initial velocity of a projectile be doubled, keeping the angle of projection same, the maximum height reached by it will

A charged particle with some initial velocity is projected in a region where non-zero electric and/or magnetic fields are present. In column I, information about the existence of electric and/or magnetic field and direction of initial velocity of charged particle are given; while in Column II, the probable path of the charged particle is mentioned. Match the entries of Column I with the entries of Column II.

$\begin{array}{cccc}& \text{Colum I}& & \text{Colum II}\\ \text{i.}& \overrightarrow{E}=0,\overrightarrow{B}\ne 0\text{and initial velocity may}& \text{a.}& \text{Straight line}\\ & \text{be at any angle with}\overrightarrow{B}.& & \\ \text{ii.}& \overrightarrow{E}=0,\overrightarrow{B}=0\text{and initial velocity may}& \text{b.}& \text{Parabola}\\ & \text{be at any angle with}\overrightarrow{E}.& & \\ \text{iii}& \overrightarrow{E}\ne 0,\overrightarrow{B}\ne 0,\overrightarrow{E}||\overrightarrow{B}\text{and initial velocity is}& \text{c.}& \text{Circular}\\ & \perp \text{to both.}& & \\ & & \text{d.}& \text{Helical path}\end{array}$

A horizontal pipeline carries water in a streamline flow. At a point where the cross-sectional area is $10{\text{cm}}^2$, the water velocity is $1{\text{ms}}^{-1}$ and pressure is $2000\text{Pa}$. The pressure of water at another point where the cross sectional area is $5{\text{cm}}^2$, is:

The horizontal range and maximum height attained by a projectile are $R$ and $H$, respectively. If a constant horizontal acceleration $a=\frac{g}{4}$ is imparted to the projectile due to wind, then its horizontal range and maximum height will be

A bullet of mass $50\text{gm}$ is fired from below onto a bob of mass $450\text{gm}$ of a long simple pendulum as shown in the figure. The bullet remains inside the bob and the bob rises through a height of $1.8\text{m}$ vertically upwards. Find the speed of the bullet.

A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

An open pipe vibrating in its fundamental frequency is suddenly closed at one end. As a result, the frequency of the third harmonic of the closed pipe is found to be higher by $100\text{Hz}$. The fundamental frequency of the open pipe is :-

In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to the $n^{th}$ mass is

Find the moment of inertia ($\text{MI}$) of an uniform rod of mass $3\text{kg}$ and length $2\text{m}$ about an axis ($y{y}^{\prime }$) perpendicular to the plane of rod and passing through it's one end ($A$) as shown in the figure.

Projection of $\overrightarrow{A}$ along the vector $\overrightarrow{B}$ is

Four students observed an ideal gas undergoing a change of state from A to B. Their observations are along four different paths shown in the figure below. Their conclusions are as follows:

$\left(P\right)$ Change in internal energy is same in $IV$ and $III$ cases, but not in $I$ and $II$

$\left(Q\right)$ Change in internal energy is same in all the four cases

$\left(R\right)$ Work done is maximum in case $I$

$\left(S\right)$ Workdone is minimum in case $II$

Which option represents correct conclusions drawn by the students?

Two rings of same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is

(Mass of each ring $=m$, radius $=r$)

A bubble of air has radius $0.2\text{mm}$ in water. If the bubble had been formed $20\text{cm}$ below the water surface on a day when the atmospheric pressure was $1.013\times {10}^5\text{Pa}$, then what would have been the total pressure inside the bubble? (surface tension of water = $73\times {10}^{-3}\text{N/m}$)

Find $F$ such that the $2\text{kg}$ body goes up with an acceleration of $2{\text{m/s}}^2$.

Take ($g=10{\text{m/s}}^2$)

At normal temperature and pressure conditions, water boils at ${100}^{\circ }C$. Deep down the mine, at what temperature will the water boil?

Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are found to be in the ratio of $3:1$. Then

Consider a rope of total mass $M$ and length $L$ suspended at rest from a fixed mount. The rope has a linear mass density that varies with height as $\lambda \left(z\right)={\lambda }_0\sin (\pi z\setminus L)$, where ${\lambda }_0$ is a constant. Constant gravitational acceleration $g$ acts downward, then constant ${\lambda }_0$ is

A cubical block of mass $m$ slides in an inclined right angled trough as shown in the figure. If the coefficients of kinetic friction between block and material composing the trough is ${\mu }_k$, find the acceleration of the block. (Both walls of the trough make an angle of 45^∘ with the inclined plane)

A ball is thrown vertically upwards with a speed of $9.8\text{m/s}$ from the top of tower. If it returns to ground in $3\text{seconds}$, find the height of tower. (Take $g=9.8{\text{m/s}}^2$)

A capacitor of capacitance $10\mu F$ is connected to a battery providing a potential difference of 10 V across the capacitor. The energy stored inside the capacitor is?

A boy walks to his school at a distance of 6 km with constant speed of 2.5 km/hour and walks back with a constant speed of 4 km/hr. His average speed for round trip expressed in km/hr, is

On the superposition of the two waves represented by equation $y_1=A\sin (\omega t-kx)$ and $y_2=A\sin (\omega t-kx+\frac{\pi }{4})$, the resultant amplitude of oscillation will be:

In an $L-R$ circuit connected to a battery of constant e.m.f $E$, switch S is closed at time t = 0. If e denotes the magnitude of induced e.m.f across inductor and i the current in the circuit at any time t. Then which of the following graphs shows the variation of $e$ with $i$ ?

Two plane mirrors. A and B are aligned parallel to each other, as shown in

the figure. A light ray is incident at an angle of 30⁰ at a point just inside one

end of A. The plane of incidence coincides with the plane of the figure. The

maximum number of times the ray undergoes reflections (including the first

one) before it emerges out is

[IIT-JEE (Screening) 2002]

Figure shows two parallel and coaxial loops. The smaller loop (radius $r$) is above the larger loop (radius $R$), by distance $x$ ($x>>R$). The magnetic fielde due to current $i$ in the larger loop is nearly constant throughout the smaller loop. Suppose that $x$ is increasing at a constant rate of $\frac{dx}{dt}=v$. The induced emf in the smaller loop is

The acceleration of a car moving in positive $x-$direction with an initial velocity of $6m/s$ is $4m/s^2$. Its velocity at $t=5sec$ is

Energy required to move a body of mass m from an orbit of radius 2R to 3R is

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to

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

The speed of sound in hydrogen gas at $\text{STP}$ is $v_o$. The speed of sound in a mixture containing $3$ parts of hydrogen gas and $2$ parts of oxygen gas at $\text{STP}$ will be

A $10\text{kg}$ ball attached at the end of a rigid massless rod of length $(L=1\text{m})$ rotates at constant speed in a horizontal circle of radius $0.5\text{m}$ with a period of $1.57\text{s}$, as shown in the figure. The force exerted by the rod on the ball is (Take $g=10{\text{ms}}^{-2}$ & $\pi =3.14$)

A cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of centre $O$ with angle $={60}^{\circ }$. If $B_1$ and $B_2$ are the magnitudes of the magnetic fields at O due to the currents in $ABC$ and ADC respectively, the ratio $\frac{B_1}{B_2}$ is