In a Young's double slit experiment, the two slits act as coherent sources of waves of equal amplitude A and wavelength
Question: In a Young's double slit experiment, the two slits act as coherent sources of waves of equal amplitude A and wavelength $\lambda$. In another experiment with the same arrangement the two slits are made to act as incoherent sources of waves of same amplitude and wavelength. If the intensity at the middle point of the screen in the first case is $\mathrm{I}_{1}$ and in the second case $\mathrm{I}_{2}$, then the ratio $\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}$ is :-4210.5Correct Option: Solu...
Read More →A liquid in a beaker has temperature
Question: A liquid in a beaker has temperature $\theta(t)$ at time $t$ and $\theta_{0}$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between $\log _{e}\left(\theta-\theta_{0}\right)$ and $t$ is :-Correct Option: , 2 Solution:...
Read More →Statement-1: On viewing the clear blue portion of the sky through a Calcite Crystal,
Question: Statement-1: On viewing the clear blue portion of the sky through a Calcite Crystal, the intensity of transmitted light varies as the crystal is rotated. Statement-1: The light coming from the sky is polarized due to scattering of sun light by particles in the atmosphere. The scattering is largest for blue light.Statement-1 is false, statement-2 is trueStatement- 1 is true, statement- 2 is falseStatement-1 is true, statement-2 true; statement- 2 is the correct explanation of statement-...
Read More →A long metallic bar is carrying
Question: A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $\mathrm{x}$ of the bar from its hot end is best described by which of the following figures ?Correct Option: , 4 Solution:...
Read More →If a simple pendulum has Significant amplitude
Question: If a simple pendulum has Significant amplitude (up to a factor of $1 /$ e of original) only in the period between $t=0 \mathrm{~s}$ to $\mathrm{t}=\tau \mathrm{s}$, then $\tau$ may be called the average life ofthe pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with " $b$ ' as the constant of proportionality, the average lifetime ofthe pendulum is (assuming damping is small) in seconds: $\frac{1}{b}$$\frac{2}{b}...
Read More →The magnitude of the magnetic field (B) due to the loop
Question: The magnitude of the magnetic field (B) due to the loop $\mathrm{ABCD}$ at the origin $(\mathrm{O})$ is :- A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius $=b$ ) and DA (radius $=a$ ) of the loop are joined by two straight wires AB and CD. A steady current $\mathrm{I}$ is flowing in the loop. Angle made by $\mathrm{AB}$ and $\mathrm{CD}$ at the origin $\mathrm{O}$ is $30^{\circ}$. Another straight thin wire with steady current $I_...
Read More →At two points P and Q on screen in Young's double slit experiment,
Question: At two points $\mathrm{P}$ and $\mathrm{Q}$ on screen in Young's double slit experiment, waves from slits $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ have a path difference of 0 and $\frac{\lambda}{4}$ respectively. the ratio of intensities at $P$ and $Q$ will be : (A) (B) (C) (D)$3: 2$$2: 1$$\sqrt{2}: 1$$4: 1$Correct Option: , 2 Solution:...
Read More →If a spring of stiffiness
Question: If a spring of stiffiness ' $\mathrm{k}$ ' is cut into two parts 'A' and ' $\mathrm{B}$ ' of length $\ell_{\mathrm{A}}: \ell_{\mathrm{B}}=2: 3$, then the stiffiness of spring ' $A$ ' is given by :- $\frac{5}{2} \mathrm{k}$$\frac{3 k}{5}$$\frac{2 k}{5}$$\mathrm{k}$Correct Option: 1 Solution:...
Read More →A solid sphere of radius
Question: A solid sphere of radius $r$ made of a soft material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass $m$ is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $\left(\frac{\mathrm{dr}}{\mathrm{r}}\right)$, is :$\frac{\mathrm{Ka}}{3 \mathrm{mg}}$$\frac{\mathrm{mg}}{3 \...
Read More →A man grows into a giant
Question: A man grows into a giant such that his linear dimensions increase by a factor of 9 . Assuming that his density remains same, the stress in the leg will change by a factor of:81$\frac{1}{81}$9$\frac{1}{9}$Correct Option: , 3 Solution:...
Read More →The density of a material in the shape of a cube
Question: The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5 \%$ and $1 \%$, the maximum error in determining the density is :-$3.5 \%$$4.5 \%$$6 \%$$2.5 \%$Correct Option: , 2 Solution:...
Read More →In an a. c. circuit, the instantaneous e.m.f.
Question: In an a. c. circuit, the instantaneous e.m.f. and current are given by e $=100 \sin 30 \mathrm{t} \mathrm{i}=20 \sin \left(30 \mathrm{t}-\frac{\pi}{4}\right)$ In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively.$\frac{1000}{\sqrt{2}}, 10$$\frac{50}{\sqrt{2}}, 0$50,050,10Correct Option: 1 Solution:...
Read More →For an RLC circuit driven with voltage of amplitude
Question: For an RLC circuit driven with voltage of amplitude $\mathrm{v}_{\mathrm{m}}$ and frequency $\mathrm{w}_{0}=\frac{1}{\sqrt{\mathrm{LC}}}$ the current exhibits resonance. The quality factor, $Q$ is given by :$\frac{\omega_{0} R}{L}$$\frac{\mathrm{R}}{\left(\omega_{0} \mathrm{C}\right)}$$\frac{\mathrm{CR}}{\omega_{0}}$$\frac{\omega_{0} L}{R}$Correct Option: , 4 Solution:...
Read More →The following observations were taken for determining
Question: The following observations were taken for determining surface tensiton $\mathrm{T}$ of water by capillary method: Diameter of capilary, $\mathrm{D}=1.25 \times 10^{-2} \mathrm{~m}$ rise of water, $\mathrm{h}=1.45 \times 10^{-2} \mathrm{~m}$ Using $g=9.80 \mathrm{~m} / \mathrm{s}^{2}$ and the simplified relation $\mathrm{T}=\frac{\text { rhg }}{2} \times 10^{3} \mathrm{~N} / \mathrm{m}$, the possible error in surface tension is closest to :$2.4 \%$$10 \%$$0.15 \%$$1.5 \%$Correct Option:...
Read More →An arc lamp requires a direct current of
Question: An arc lamp requires a direct current of $10 \mathrm{~A}$ at $80 \mathrm{~V}$ to function. If it is connected to a $220 \mathrm{~V}(\mathrm{rms}$ ), $50 \mathrm{~Hz}$ AC supply, the series inductor needed for it to work is close to :-$0.065 \mathrm{H}$$80 \mathrm{H}$$0.08 \mathrm{H}$$0.044 \mathrm{H}$Correct Option: 1 Solution:...
Read More →An arc lamp requires a direct current of
Question: An arc lamp requires a direct current of $10 \mathrm{~A}$ at $80 \mathrm{~V}$ to function. If it is connected to a $220 \mathrm{~V}(\mathrm{rms}$ ), $50 \mathrm{~Hz}$ AC supply, the series inductor needed for it to work is close to :-$0.065 \mathrm{H}$$80 \mathrm{H}$$0.08 \mathrm{H}$$0.044 \mathrm{H}$Correct Option: Solution:...
Read More →Two particles are executing simple harmonic motion of the same amplitude
Question: Two particles are executing simple harmonic motion of the same amplitude A and frequency $\omega$ along the $\mathrm{x}$-axis. Their mean position is separated by distance $\mathrm{X}_{0}\left(\mathrm{X}_{0}\mathrm{A}\right)$. If the maximum separation between them is $\left(X_{0}+A\right)$, the phase difference between their motion is :- $\frac{\pi}{4}$$\frac{\pi}{6}$$\frac{\pi}{2}$$\frac{\pi}{3}$Correct Option: , 4 Solution:...
Read More →A particle is moving
Question: A particle is moving with a uniform speed in a circular orbit of radius $\mathrm{R}$ in a central force inversely proportional to the $n^{\text {th }}$ power of $R$. If the period of rotation of the particle is $T$, then,$T \propto R^{\frac{n}{2}+1}$$T \propto R^{(\mathrm{n}+1) / 2}$$\mathrm{T} \propto \mathrm{R}^{\mathrm{n} / 2}$$T \propto R^{3 / 2}$ for any $n$Correct Option: , 2 Solution:...
Read More →An LCR circuit is equivalent to a damped pendulum.
Question: An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to $\mathrm{Q}_{0}$ and then connected to the $\mathrm{L}$ and $\mathrm{R}$ as shown below. If a student plots graphs of the square of maximum charge $\left(\mathrm{Q}_{\text {Max }}^{2}\right)$ on the capacitor with time $(\mathrm{t})$ for two different values $\mathrm{L}_{1}$ and $\mathrm{L}_{2}\left(\mathrm{~L}_{1}\mathrm{L}_{2}\right)$ of $L$ then which of the following represents this gra...
Read More →Two cars of masses
Question: Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is :-$1: 1$$\mathrm{m}_{1} \mathrm{r}_{1}: \mathrm{m}_{2} \mathrm{r}_{2}$$\mathrm{m}_{1}: \mathrm{m}_{2}$$r_{1}: r_{2}$Correct Option: , 4 Solution:...
Read More →A student measures the time period of 100 oscillations
Question: A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is $90 \mathrm{~s}, 91 \mathrm{~s}, 95 \mathrm{~s}$ and $92 \mathrm{~s}$. If the minimum division in the measuring clock is $1 \mathrm{~s}$, then the reported mean time should be :-$92 \pm 3 \mathrm{~s}$$92 \pm 2 \mathrm{~s}$$92 \pm 5.0 \mathrm{~s}$$92 \pm 1.8 \mathrm{~s}$Correct Option: , 2 Solution:...
Read More →A mass M, attached to a horizontal spring, executes S.H.M. with amplitude
Question: A mass M, attached to a horizontal spring, executes S.H.M. with amplitude $A_{1}$. When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude $A_{2}$. The ratio of $\left(\frac{A_{1}}{A_{2}}\right)$ is :- $\left(\frac{\mathrm{M}}{\mathrm{M}+\mathrm{m}}\right)^{1 / 2}$$\left(\frac{\mathrm{M}+\mathrm{m}}{\mathrm{M}}\right)^{1 / 2}$$\frac{M}{M+m}$$\frac{\mathrm{M}+\mathrm{m}}{\mathrm{M}}$Correct Option: , 2 So...
Read More →A point P moves in counter
Question: A point $P$ moves in counter clockwise direction on a circular path as shown in the figure. The movement of ' $\mathrm{P}^{\prime}$ is such that it sweeps out a length $\mathrm{s}=\mathrm{t}^{3}+5$, where $\mathrm{s}$ is in metres and $\mathrm{t}$ is in seconds. The radius of the path is $20 \mathrm{~m}$. The acceleration of ' $P^{\prime}$ when $t=2 \mathrm{~s}$ is nearly : $14 \mathrm{~m} / \mathrm{s}^{2}$$13 \mathrm{~m} / \mathrm{s}^{2}$$12 \mathrm{~m} / \mathrm{s}^{2}$$7.2 \mathrm{~...
Read More →In an LCR circuit as shown below both switches are open initially.
Question: In an $L C R$ circuit as shown below both switches are open initially. Now switch $S_{1}$ is closed, $S_{2}$ kept open, ( $\mathrm{q}$ is charge on the capacitor and $\tau=\mathrm{RC}$ is Capacitive time constant). Which of the following statement is correct? Work done by the battery is half of the energy dissipated in the resistorAt $\mathrm{t}=\tau, \mathrm{q}=\mathrm{CV} / 2$$\mathrm{At} \mathrm{t}=2 \tau, \mathrm{q}=\mathrm{CV}\left(1-\mathrm{e}^{-2}\right)$At $\mathrm{t}=\frac{\ta...
Read More →A screw gauge with a pitch of
Question: A screw gauge with a pitch of $0.5 \mathrm{~mm}$ and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the $45^{\text {th }}$ division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is $0.5 \mathrm{~mm}$ and the $25^{\text {th ...
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