For a pacticle in uniform circular motion,
Question: For a pacticle in uniform circular motion, the acceleration $\vec{a}$ at a point $P(R, \theta)$ on the circle of radius $R$ is (Here $\theta$ is measured from the $x$-axis).$\frac{v^{2}}{R} \hat{i}+\frac{v^{2}}{R} \hat{j}$$-\frac{\mathrm{v}^{2}}{\mathrm{R}} \cos \theta \hat{\mathrm{i}}+\frac{\mathrm{v}^{2}}{\mathrm{R}} \sin \theta \hat{\mathrm{j}}$$-\frac{v^{2}}{R} \sin \theta \hat{i}+\frac{v^{2}}{R} \cos \theta \hat{j}$$-\frac{\mathrm{v}^{2}}{\mathrm{R}} \cos \theta \hat{\mathrm{i}}-\...
Read More →A fully charged capacitor C with intial charge
Question: A fully charged capacitor $\mathrm{C}$ with intial charge $\mathrm{q}_{0}$ is connected to a coil of self inductance $\mathrm{L}$ at $\mathrm{t}=0$. The time at which the energy is stored equally between the electric and the magnetic fields is :-$2 \pi \sqrt{\mathrm{LC}}$$\sqrt{\mathrm{LC}}$$\pi \sqrt{\mathrm{LC}}$$\frac{\pi}{4} \sqrt{\mathrm{LC}}$Correct Option: , 4 Solution:...
Read More →The period of oscillation of a simple pendulum
Question: The period of oscillation of a simple pendulum is $T=2 \pi \sqrt{\frac{L}{g}}$. Measured value of $L$ is $20.0 \mathrm{~cm}$ known to $1 \mathrm{~mm}$ accuracy and time for 100 oscillations of the pendulum is found to be $90 \mathrm{~s}$ using a wrist watch of 1 s resolution. The accuracy in the determination of $g$ is :$1 \%$$5 \%$2\%$3 \%$Correct Option: , 4 Solution:...
Read More →Prove the following
Question: In a series $\mathrm{LCR}$ circuit $\mathrm{R}=200 \Omega$ and the voltage and the frequency of the main supply is $220 \mathrm{~V}$ and $50 \mathrm{~Hz}$ respectively. On taking out the capacitance from the circuit the current lages behind the voltage by $30^{\circ}$. On taking out the inductor from the circuit the current leads the voltage by $30^{\circ}$. The power dissipated in the LCR circuit is :$242 \mathrm{~W}$$305 \mathrm{~W}$$210 \mathrm{~W}$Zero WCorrect Option: 1 Solution:...
Read More →A student measured the length of a rod and
Question: A student measured the length of a rod and wrote it as $3.50 \mathrm{~cm}$. Which instrument did he use to measure it ?A screw gauge having 100 divisions in the circular scale and pitch as $1 \mathrm{~mm}$.A screw gauge having 50 divisions in the circular scale and pitch as $1 \mathrm{~mm}$A meter scaleA vernier calliper where the 10 divisions in vernier scale matches with 9 division in main scale and main scale has 10 divisions in $1 \mathrm{~cm}$.Correct Option: , 4 Solution: Least c...
Read More →Solve this following
Question: If $x, v$ and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $\mathrm{T}$, then, which of the following does not change with time ? $a T+2 \pi v$$\frac{\mathrm{aT}}{\mathrm{v}}$$a^{2} T^{2}+4 \pi^{2} v^{2}$$\frac{a T}{x}$Correct Option: , 3, 4 Solution:...
Read More →The current voltage relation of diode is given by
Question: The current voltage relation of diode is given by $\mathrm{I}=\left(\mathrm{e}^{1000 \mathrm{~V} / \mathrm{T}}-1\right) \mathrm{mA}$, where the applied voltage $\mathrm{V}$ is in volts and the temperature $\mathrm{T}$ is in degree Kelvin. If a student makes an error measuring $\pm 0.01 \mathrm{~V}$ while measuring the current of $5 \mathrm{~mA}$ at $300 \mathrm{~K}$, what will be error in the value of current in mA?$0.5 \mathrm{~mA}$$0.05 \mathrm{~mA}$$0.2 \mathrm{~mA}$$0.02 \mathrm{~m...
Read More →In a collinear collision,
Question: In a collinear collision, a particle with an initial speed $v_{0}$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50 \%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :$\sqrt{2} \mathrm{v}_{0}$$\frac{v_{0}}{2}$$\frac{\mathrm{v}_{0}}{\sqrt{2}}$$\frac{V_{0}}{4}$Correct Option: 1 Solution:...
Read More →As the beam enters the medium
Question: As the beam enters the medium, it will :- travel as a cylindrical beamdivergeconvergediverge near the axis and converge near the peripheryCorrect Option: , 3 Solution:...
Read More →Resistance of a given wire is obtained by measuring
Question: Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3 \%$ each, then error in the value of resistance of the wire is :-$3 \%$$6 \%$zero$1 \%$Correct Option: , 2 Solution: $R=\frac{V}{I} \Rightarrow \frac{\Delta R}{R}=\pm\left(\frac{\Delta V}{V}+\frac{\Delta I}{I}\right)$ $=\pm(3+3) \%=\pm 6 \%$...
Read More →It is found that if a neutron
Question: It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $\mathrm{p}_{d}$; while for its similar collision with carbon nucleus at rest, fractional loss of energy is $p_{c^{*}}$. The values of $p_{d}$ and $p_{c}$ are respectively :$(.28, .89)$$(0,0)$$(0,1)$$(.89, .28)$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: A granite rod of $60 \mathrm{~cm}$ length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ and its Young's modulus is $9.27 \times 10^{10} \mathrm{~Pa}$. What will be the fundamental frequency of the longitudinal vibrations? $2.5 \mathrm{kHz}$$10 \mathrm{kHz}$$7.5 \mathrm{kHz}$$5 \mathrm{kHz}$Correct Option: , 4 Solution:...
Read More →The speed of the light in the medium is
Question: The speed of the light in the medium is :- maximum on the axis of the beamminimum on the axis of the beamthe same everywhere in the beamdirectly proportional to the intensity ICorrect Option: , 2 Solution: Intensity is maximum at the axis of the cylindrical beam. Hence $\mu$ is maximum at the axis due to the relation $\mu=\mu_{0}+\mu_{2}$ I and $v \propto \frac{1}{\mu}$...
Read More →A spectrometer gives the following reading
Question: A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading : $58.5$ degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to $0.5$ degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data : 59 degree$58.59$ degree$58.77$ degree$58.65$ degreeCorrect Option: , 4 Solution:...
Read More →An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency
Question: An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $10 \mathrm{GHz}$. What is the frequency of the microwave measured by the observer? (speed of light $=3 \times 10^{8} \mathrm{~ms}^{-1}$ ) $17.3 \mathrm{GHz}$$15.3 \mathrm{GHz}$$10.1 \mathrm{GHz}$$12.1 \mathrm{GHz}$Correct Option: 1 Solution:...
Read More →Distance of the centre of mass
Question: Distance of the centre of mass of a solid uniform cone from its vertex is $z_{0}$. If the radius of its base is $\mathrm{R}$ and its height is $\mathrm{h}$ then $\mathrm{z}_{0}$ is equal to :-$\frac{5 h}{8}$$\frac{3 h^{2}}{8 R}$$\frac{h^{2}}{4 R}$$\frac{3 \mathrm{~h}}{4}$Correct Option: , 4 Solution:...
Read More →A screw gauge gives the following reading
Question: A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : $0 \mathrm{~mm}$. Circular scale reading : 52 divisions Given that $1 \mathrm{~mm}$ on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above date is :- $0.026 \mathrm{~cm}$$0.005 \mathrm{~cm}$$0.52 \mathrm{~cm}$$0.052 \mathrm{~cm}$Correct Option: , 4 Solution:...
Read More →A particle of mass
Question: A particle of mass $m$ moving in the $x$ direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the y direction with speed $v$. If the collisions perfectly inelastic, the percentage loss in the energy during the collision is close to:$56 \%$$62 \%$$44 \%$$50 \%$Correct Option: 1 Solution:...
Read More →A pipe open at both ends has a fundamental frequency
Question: A pipe open at both ends has a fundamental frequency $\mathrm{f}$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequencty of the air column is now :- $\mathrm{f}$$\frac{\mathrm{f}}{2}$$\frac{3 f}{4}$$2 f$Correct Option: 1 Solution:...
Read More →This question has Statement
Question: This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I : A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as $f\left(\frac{1}{2} m v^{2}\right)$ then $f=\left(\frac{m}{M+m}\right)$. Statement - II : Maximum energy loss occurs when the particles get stuck together as a result of the col...
Read More →The initial shape of the wavefront of the beam is
Question: The initial shape of the wavefront of the beam is :-planarconvexconcaveconvex near the axis and concave near the peripheryCorrect Option: 1 Solution: For a parallel beam wavefronts are plane wave fronts....
Read More →The respective number of significant figures
Question: The respective number of significant figures for the numbers $23.023,0.0003$ and $2.1 \times 10^{-3}$ are :-$4,4,2$$5,1,2$$5,1,5$$5,5,2$Correct Option: , 3 Solution: $5,1,2$ resp....
Read More →In an optics experiment,
Question: In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and the image distance $v$, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of $45^{\circ}$ with the $x$-axis meets the experimental curve at $P$. The coordinates of $P$ will be...
Read More →A train is moving on a straight track with speed
Question: A train is moving on a straight track with speed $20 \mathrm{~ms}^{-1}$. It is blowing its whistle at the frequency of $1000 \mathrm{~Hz}$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $=320 \mathrm{~ms}^{-1}$ ) close to :- $18 \%$$24 \%$$6 \%$$12 \%$Correct Option: , 4 Solution:...
Read More →A mixture of light consisting of wavelength
Question: A mixture of light, consisting of wavelength $590 \mathrm{~nm}$ and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4 th bright fringe of the unknown light. From this data, the wavelength of the unknown light is :- $442.5 \mathrm{~nm}$$776.8 \mathrm{~nm}$$393.4 \mathrm{~nm}$$885....
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