A block of mass

Question: A block of mass $\mathrm{m}$ is connected to another block of mass $M$ by a spring (massless) of spring constant $\mathrm{k}$. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force $\mathrm{F}$ starts acting on the block of mass $\mathrm{M}$ to pull it. Find the force on the block of mass $m$ :-$\frac{\mathrm{mF}}{\mathrm{M}}$$\frac{(M+m) F}{m}$$\frac{m F}{(m+M)}$$\frac{M F}{(m+M)}$Correct Option: , 3 Sol...

A player caught a cricket ball

Question: A player caught a cricket ball of mass $150 \mathrm{~g}$ moving at a rate of $20 \mathrm{~m} / \mathrm{s}$. If the catching process is completed in $0.1 \mathrm{~s}$., the force of the blow exerted by the ball on the hand of the player is equal to-$150 \mathrm{~N}$$3 \mathrm{~N}$$30 \mathrm{~N}$$300 \mathrm{~N}$Correct Option: , 3 Solution:...

A block is kept on a frictionless

Question: A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration a to keep the block stationary. Then a is equal to- $\mathrm{g} / \tan \alpha$$g \operatorname{cosec} \alpha$$\mathrm{g}$$\operatorname{gtan} \alpha$Correct Option: , 4 Solution:...

Two masses

Question: Two masses $\mathrm{m}_{1}=5 \mathrm{~kg}$ and $\mathrm{m}_{2}=4.8 \mathrm{~kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when they are free to move ? $\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$ $0.2 \mathrm{~m} / \mathrm{s}^{2}$$9.8 \mathrm{~m} / \mathrm{s}^{2}$$5 \mathrm{~m} / \mathrm{s}^{2}$$4.8 \mathrm{~m} / \mathrm{s}^{2}$Correct Option: 1 Solution:...

A block of mass

Question: A block of mass $\mathrm{M}$ is pulled along a horizontal frictionless surface by a rope of mass $\mathrm{m}$. If a force $\mathrm{P}$ is applied at the free end of the rope, the force exerted by the rope on the block is$\frac{\mathrm{Pm}}{\mathrm{M}+\mathrm{m}}$$\frac{\mathrm{Pm}}{\mathrm{M}-\mathrm{m}}$$\mathrm{P}$$\frac{\mathrm{PM}}{\mathrm{M}+\mathrm{m}}$Correct Option: , 4 Solution:...

Three forces start acting

Question: Three forces start acting simultaneously on a particle moving with velocity $\vec{v}$. These forces are represented in magnitude and direction by the three sides of a triangle $\mathrm{ABC}$ (as shown). The particle will now move with velocity- Less than $\vec{v}$greater than $\vec{v}$$|\mathrm{v}|$ in the direction of largest force $\mathrm{BC}$$\vec{v}$, remaining unchangedCorrect Option: , 4 Solution:...

A rocket which has a mass

Question: A rocket which has a mass of $3.5 \times 10^{4} \mathrm{~kg}$ is blasted upwards with an initial acceleration of $10 \mathrm{~m} / \mathrm{s}^{2}$. Then the initial thrust of the blast is-$3.5 \times 10^{5} \mathrm{~N}$$7.0 \times 10^{5} \mathrm{~N}$$14.0 \times 10^{5} \mathrm{~N}$$1.75 \times 10^{5} \mathrm{~N}$Correct Option: , 2 Solution:...

A silver atom in a solid oscillates in simple harmonic motion in some direction

Question: A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12} / \mathrm{sec}$. What is the force constant of the bonds connecting one atom with the other ? (Mole wt. of silver $=108$ and Avagadro number $=6.02 \times 10^{23} \mathrm{gm} \mathrm{mole}^{-1}$ ) $7.1 \mathrm{~N} / \mathrm{m}$$2.2 \mathrm{~N} / \mathrm{m}$$5.5 \mathrm{~N} / \mathrm{m}$$6.4 \mathrm{~N} / \mathrm{m}$Correct Option: 1 Solution:...

A particle is executing simple harmonic motion with a time period T.

Question: A particle is executing simple harmonic motion with a time period T. AT time $t=0$, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like Correct Option: , 2 Solution:...

The dipole moment of a circular loop carrying a current

Question: The dipole moment of a circular loop carrying a current $\mathrm{I}$, is $\mathrm{m}$ and the magnetic field at the centre of the loop is $\mathrm{B}_{1}$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_{2}$. The ratio $\frac{B_{1}}{B_{2}}$ is : $\sqrt{3}$$\sqrt{2}$$\frac{1}{\sqrt{2}}$2Correct Option: , 2 Solution:...

A spring balance

Question: A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $49 \mathrm{~N}$, when the lift is stationary. If the lift moves downward with an acceleration of $5 \mathrm{~m} / \mathrm{s}^{2}$, the reading of the spring balance will be$24 \mathrm{~N}$$74 \mathrm{~N}$$15 \mathrm{~N}$$49 \mathrm{~N}$Correct Option: 1 Solution:...

An electron, a proton and an alpha particle having

Question: An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $\mathrm{r}_{\mathrm{e}}, \mathrm{r}_{\mathrm{p}}, \mathrm{r}_{\alpha}$ respectively in a uniform magnetic field $\mathrm{B}$. The relation between $\mathrm{r}_{\mathrm{e}}, \mathrm{r}_{\mathrm{p}}, \mathrm{r}_{\alpha}$ is:- $\mathrm{r}_{\mathrm{e}}\mathrm{r}_{\mathrm{p}}=\mathrm{r}_{\alpha}$$\mathrm{r}_{\mathrm{e}}\mathrm{r}_{\mathrm{p}}\mathrm{r}_{\alpha}$$\mathrm{r}_{\ma...

Two identical wires

Question: Two identical wires $\mathrm{A}$ and $\mathrm{B}$, each of length ' $T$ ', carry the same current I. Wire $\mathrm{A}$ is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side ' $a$ '. If $B_{A}$ and $B_{B}$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{B_{A}}{B_{B}}$ is :$\frac{\pi^{2}}{8 \sqrt{2}}$$\frac{\pi^{2}}{8}$$\frac{\pi^{2}}{16 \sqrt{2}}$$\frac{\pi^{2}}{16}$Correct Option: 1 Solution:...

A particle performs simple harmonic motion with amplitude A.

Question: A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance $\frac{2 \mathrm{~A}}{3}$ from equilibrium position. The new amplitude of the motion is :- $\frac{7 \mathrm{~A}}{3}$$\frac{\mathrm{A}}{3} \sqrt{41}$$3 \mathrm{~A}$$A \sqrt{3}$Correct Option: 1 Solution:...

A rectangular loop of sides

Question: A rectangular loop of sides $10 \mathrm{~cm}$ and $5 \mathrm{~cm}$ carrying a current I of $12 \mathrm{~A}$ is place in different orientations as shown in the figures below : If there is a uniform magnetic field of $0.3 \mathrm{~T}$ in the positive $\mathrm{z}$ direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium ?(b) and (d), respectively(b) and (c), respectively(a) and (b), respectively(a) and (c), respectivelyCorrect Option: 1 So...

A light spring balance hangs

Question: A light spring balance hangs from the hook of the other light spring balance and a block of mass M $\mathrm{kg}$ hangs from the former one. Then the true statement about the scale reading is-both the scales read M kg eachthe scale of the lower one reads M kg and of the upper one zeroThe reading of the two scales can be anything but the sum of the readings will be $\mathrm{M} \mathrm{kg}$both the scales read $\mathrm{M} / 2 \mathrm{~kg}$Correct Option: 1 Solution:...

Two long current carrying thin wires,

Question: Two long current carrying thin wires, both with current I, are held by the insulating threads of length $\mathrm{L}$ and are in equilibrium as shown in the figure, with threads making an angle ' $\theta$ ' with the vertical. If wires have mass $\lambda$ per unit length then the value of $\mathrm{I}$ is :- ( $g=$ gravitational acceleration) $2 \sqrt{\frac{\pi \mathrm{gL}}{\mu_{0}} \tan \theta}$$\sqrt{\frac{\pi \lambda \mathrm{gL}}{\mu_{0}} \tan \theta}$$\sin \theta \sqrt{\frac{\pi \lamb...

A conductor lies along the

Question: A conductor lies along the $\mathrm{z}$-axis at $-1.5 \leq \mathrm{z}1.5 \mathrm{~m}$ and carries a fixed current of $10.0 \mathrm{~A}$ in $-\hat{a}_{z}$ direction (see figure). For a field $\overrightarrow{\mathrm{B}}=3.0 \times 10^{-4} \mathrm{e}^{-0.2 \mathrm{a}} \hat{\mathrm{a}}_{\mathrm{y}} \mathrm{T}$, find the power required to move the conductor at constant speed to $\mathrm{x}=2.0 \mathrm{~m}, \mathrm{y}=0 \mathrm{~m}$ in $5 \times 10^{-3} \mathrm{~s}$. Assume parallel motion ...

For a simple pendulum, a graph is plotted between its kinetic energy

Question: For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement $\mathrm{d}$. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale) Correct Option: , 4 Solution:...

A charge Q is uniformly distributed over the surface of non-conducting

Question: A charge $Q$ is uniformly distributed over the surface of non-conducting disc of radius $R$. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation a magnetic field of induction $B$ is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic inductio...

Unpolarized light of intensity I passes through an ideal polarizer A.

Question: Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer $\mathrm{B}$ is placed behind $\mathrm{A}$. The intensity of light beyond $\mathrm{B}$ is found to be $\frac{1}{2}$. Now another identical polarizer $\mathrm{C}$ is placed between $\mathrm{A}$ and $\mathrm{B}$. The intensity beyond $\mathrm{B}$ is now found to be $\frac{\mathrm{I}}{8}$. The angle between polarizer $\mathrm{A}$ and $\mathrm{C}$ is :$30^{\circ}$$45^{\circ}$$60^{\circ}$$0^{\c...

Question: Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer $\mathrm{B}$ is placed behind $\mathrm{A}$. The intensity of light beyond $\mathrm{B}$ is found to be $\frac{1}{2}$. Now another identical polarizer $\mathrm{C}$ is placed between $\mathrm{A}$ and $\mathrm{B}$. The intensity beyond $\mathrm{B}$ is now found to be $\frac{\mathrm{I}}{8}$. The angle between polarizer $\mathrm{A}$ and $\mathrm{C}$ is :$30^{\circ}$$45^{\circ}$$60^{\circ}$$0^{\c...

A thin circular disk of radius R is uniformly charged

Question: A thin circular disk of radius $R$ is uniformly charged with density $\sigma0$ per unit area. The disk rotates about its axis with a uniform angular speed $\omega$. The magnetic moment of the disk is :-$2 \pi R^{4} \sigma \omega$$\pi R^{4} \sigma \omega$$\frac{\pi \mathrm{R}^{4}}{2} \sigma \omega$$\frac{\pi R^{4}}{4} \sigma \omega$Correct Option: , 4 Solution:...

The angular width of the central maximum in a single slit diffraction pattern is

Question: The angular width of the central maximum in a single slit diffraction pattern is $60^{\circ}$. The width of the slit is $1 \mu \mathrm{m}$. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance $50 \mathrm{~cm}$ from the slits. If the observed fringe width is $1 \mathrm{~cm}$, what is slit separation distance? (i.e. distance between the centres of each slit.)$50 \mu \mathrm{m...

The mass of a hydrogen molecule

Question: The mass of a hydrogen molecule is $3.32 \times 10^{-27} \mathrm{~kg}$. If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2 \mathrm{~cm}^{2}$ at an angle of $45^{\circ}$ to the normal, and rebound elastically with a speed of $10^{3} \mathrm{~m} / \mathrm{s}$, then the pressure on the wall is nearly :$4.70 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$$2.35 \times 10^{2} \mathrm{~N} / \mathrm{m}^{2}$$4.70 \times 10^{2} \mathrm{~N} / \mathrm{m}^{2}$$2.35 \times 10^{3...