Explore topic-wise InterviewSolutions in Current Affairs.

Find the $\text{MOI}$ of a uniform square plate of side length $a=10\text{m}$ and mass $5\text{kg}$ about an axis passing through its centre as shown in figure. $(\theta ={30}^{\circ })$.

Find the average rate of change of density with respect to the radius of a sphere in the interval [2, 5], where the density in terms of radius, r, is given by $d\left(r\right)=3r^3+9$

A particle A moves along a circle of radius $R=10cm$ so that its radius vector $\overrightarrow{r}$ relative to O rotates with constant angular velocity $\omega =0.2rad/s$. Find the magnitude of the velocity of the particle and its total acceleration.

The velocities of three molecules are $3v,4v$ and $12v$ respectively. Their root mean square speed will be

Air is filled at ${60}^{\circ }\text{C}$ in a vessel of open mouth. The vessel is heated to a temperature $T$, so that $\frac{1}{4}\text{th}$ part of the air escapes. Assuming the volume of the vessel remains constant, the value of $T$ is

A stone is dropped into a well in which the level of water is $h$ below the top of the well. If $v$ is velocity of sound, the time $T$ after which the splash is heard is given by

A capacitor is charged to $10\mu C$ and is at potential 5V. This capacitor is now isolated from any circuit. Now a dielectric of dielectric constant k=3 is placed between the plates such that there is no empty space left between the plates. What is the change in energy of the capacitor?

A car is moving along a circular path of radius $500m$ with a speed of $30m/s$. If at some instant, its speed increases at the rate of $2m/s^2$, then at that instant, the magnitude of resultant acceleration will be

One end of a massless spring of spring constant $100N/m$ is fixed at the centre of a frictionless horizontal table and the other end is connected to a body of mass $7kg$ lying on the table at rest. The spring has a natural length of $2m$. If the spring remains horizontal and mass is made to rotate at an angular speed of $1rad/s$, then find the elongation in the spring, assuming the elongation to be small compared to the natural length of the spring.

For the circuit shown in below figure, current in the inductor is $0.8\text{A}$ while in the capacitor is $0.6\text{A}$. What is the current drawn from the source?

The $P-V$ diagram of $2\text{gm}$ of helium gas for a certain process is shown in the figure. Find the amount of heat given to the gas during the process ?

With what acceleration $a$ should the bigger box shown in the figure descend so that the block of mass $M$ exerts a force $\frac{Mg}{4}$ on the floor of the box?
(Hint:- Use the concept of pseudo-force)

A wall of thickness $0.6\text{m}$ width has a normal area $1.5{\text{m}}^2$ and is made up of a material of thermal conductivity $0.4\text{W/mK}$. The temperature difference between the two sides is ${800}^{\circ }\text{C}.$. Find the thermal resistance of the wall.

A block of mass $m$ is kept on an inclined plane of a lift moving down with acceleration of $2{\text{m/s}}^2$. What should be the coefficient of friction for the block to move down with constant velocity relative to lift?

Two simple harmonic motions are represented by the equations $y_1=0.1\sin (100\pi t+\frac{\pi }{3})$ and $y_2=0.1\cos \pi t$. The phase difference of the velocity of particle $1$ with respect to the velocity of particle $2$ is

A train accelerates from $36\text{km/h}$ to $54\text{km/h}$ in $5\text{s}$ then average acceleration of the train is

A monoatomic gas at pressure $P$ and volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. Then the final pressure of the gas is (take $\gamma =\frac{5}{3})$

A monkey is descending from the branch of a tree with constant acceleration. If the breaking strength of branch is $75\%$ of the weight of the monkey, the minimum acceleration with which monkey can slide down without breaking the branch is

The two rods shown in figure have identical geometrical dimensions. They are in contact with two heat baths at temperatures ${100}^{\circ }C$ and $0^{\circ }C$. The temperature of the junction is ${70}^{\circ }C$. Find the temperature of the junction if the ods are interchanged.

A gas is present at a pressure of $2\text{atm}$. What should be the increase in pressure so that the volume of the gas can be decreased to $\frac{1}{4}\text{th}$ of the initial value, if the temperature is maintained constant?

A force acts on a $10\text{g}$ particle in such a way that the position of particle as a function of time is given by $x=3+4t^2$, where $x$ is in $\text{m}$ and $\text{t}$ is in seconds. The work done during first $7$ seconds is

When an small object is placed at a distance $x_1$ and $x_2$ from a lens on its principal axis in the same side, then real image and a virtual image are formed respectively having same magnitude of transverse magnification. Then, the focal length of the lens is

Two identical hollow spheres having mass $m=3\text{kg}$ and radius $r=1\text{m}$ are performing combined translational and rotational motion as shown in the figure. If $\omega =2\text{rad/s}$,$v_{com}=3\text{m/s}$ and ${\omega }^{\prime }=3\text{rad/s},v_{com}^{{}^{\prime }}=2\text{m/s}$, find the ratio of their kinetic energies.

A particle is projected from the ground at an angle of ${60}^{\circ }$ with horizontal with speed $u=20m/s$. The radius of curvature of the path of the particle, when its velocity makes an angle of ${30}^{\circ }$ with horizontal is
(Take $g=10m/s^2$)

A ball is moving with uniform speed in a circular path of radius $3\text{m}$ at a rate of $5\text{revolution/minute}$. Find the average speed of the ball.

A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness $\frac{t}{4}$ Then the relation between the moment of inertia about their natural axis $I_X$ and $I_Y$ is

The figure shows an object that is cut in to two pieces by a plane passing through the centre of mass. The masses of the two pieces are $m_{1}and{m}_2$. Which of the following can be concluded regarding the masses $m_{1}and{m}_2$?

A uniform heavy chain of length 'a' initially has length 'b' hanging off of a table. The remaining part of chain a - b, is coiled on the table. If the chain is released, the velocity of the chain when the last link leaves the table is

Which of the following is a good approximation of one dimensional motion

Swimming is possible on account of

A ball of mass $m$ is projected upward from a tower with velocity $30\text{m/s}$ and at the same time, another ball of mass $2m$ is dropped from rest from the same tower. Find the displacement of the $COM$ in $2\text{s}$. [Take $g=10{\text{m/s}}^2$]

If the radius of a solid sphere is 35 cm. The radius of gyration when the axis along a tangent is

A thin, rectangular film of liquid is extended from $(2\text{cm}\times 3\text{cm})$ to $(4\text{cm}\times 6\text{cm})$. If the work done in the process is $6\times {10}^{-4}\text{J}$, the value of surface tension of the liquid is

If $A=\{x:x=4k+1,k\in W\text{and}k\le 12\}$ and $B=\{x:x=5^k,k\in W\text{and}k\le 6\}$, then $n\left(A\Delta B\right)$ is

Two metallic strips each of thickness ${10}^{-4}\text{m}$ are riveted together. Their coefficients of linear expansion are ${10}^{-5}{}^{\circ }{\text{C}}^{-1}$ and $2\times {10}^{-5}{}^{\circ }{\text{C}}^{-1}$. If they are heated through a temperature change of $50{}^{\circ }\text{C}$, the bimetallic strip will bend to form an arc of radius

Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the lower frequency in the setting is 360 Hz. the beat frequency when the two wires are sounded together is

Four particles, each of mass m, are placed at the corners of a square of side a in the x-y plane. If the origin of the coordinate system is taken at the point of intersection of the diagonals of the square, the coordinates of the centre of mass of the system are

Find the derivative of $x^5$

A boat is rowed perpendicular to river flow at the rate of $4.5\text{km/hr}$. The river flows at the rate of $6\text{km/hr}$. The speed of boat in $\text{m/s}$ is

Choose incorrect statement:

Vijay has to go to office from home. He travels the first half of the distance at speed of 30 km/hr. For the remaining distance he travels at 10 km/hr for half the time and at 20 km/hr for the rest. Find his average speed.

There are four solid balls with their centres at the four corners of a square of side $a$. The mass of each sphere is $m$ and radius $r$. Find the moment of inertia of the system about one of the sides of the square.

For the planet-sun system identify the correct statement

A mass $m$ of lead shot is placed at the bottom of a vertical cardboard cylinder that is 1.5 m long and closed at both ends. The cylinder is suddenly inverted so that the shot falls 1.5 m. If this process is repeated quickly 100 times, assuming no heat is dissipated or lost, the temperature of the shot will increase by(specific heat of lead = 0.03 cal/g°C)