Two wires of same length and thickness having
Question: Two wires of same length and thickness having specific resistances $6 \Omega \mathrm{cm}$ and $3 \Omega \mathrm{cm}$ respectively are connected in parallel. The effective resistivity is $\rho \Omega \mathrm{cm}$. The value of $\rho$, to the nearest integer, is_______. Solution: $\because$ in parallel $\frac{\rho \ell}{2 \mathrm{~A}}=\frac{\rho_{1} \frac{\ell}{\mathrm{A}} \times \rho_{2} \frac{\ell}{\mathrm{A}}}{\rho_{1} \frac{\ell}{\mathrm{A}}+\rho_{2} \frac{\ell}{\mathrm{A}}}$ $\frac{...
Read More →Two discs have moments
Question: Two discs have moments of intertia $I_{1}$ and $I_{2}$ about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $\omega_{1}$ and $\omega_{2}$ respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by:$\frac{\mathrm{I}_{1} \mathrm{I}_{2}}{\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right)}\left(\omega_{1}-\omega_{2}\right)^{2}...
Read More →Consider a 72 cm long wire AB as shown in the figure.
Question: Consider a $72 \mathrm{~cm}$ long wire $\mathrm{AB}$ as shown in the figure. The galvanometer jockey is placed at $P$ on $A B$ at a distance $x \mathrm{~cm}$ from $A$. The galvanometer shows zero deflection. The value of $x$, to the nearest integer, is Solution: In Balanced conditions $\frac{12}{6}=\frac{x}{72-x}$ $x=48 \mathrm{~cm}$...
Read More →Water drops are falling
Question: Water drops are falling from a nozzle of a shower onto the floor, from a height of $9.8 \mathrm{~m}$. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.$4.18 \mathrm{~m}$$2.94 \mathrm{~m}$$2.45 \mathrm{~m}$$7.35 \mathrm{~m}$Correct Option: , 4 Solution: $\mathrm{H}=\frac{1}{2} \mathrm{gt}^{2}$ $\frac{9.8 \times 2}{9.8...
Read More →Red light differs from blue light as they have:
Question: Red light differs from blue light as they have:Different frequencies and different wavelengthsDifferent frequencies and same wavelengthsSame frequencies and same wavelengthsSame frequencies and different wavelengthsCorrect Option: 1 Solution: Red light and blue light have different wavelength and different frequency....
Read More →A particle of mass
Question: A particle of mass $\mathrm{m}$ is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r=\frac{L}{\sqrt{2}}$. The speed of particle will be : $\sqrt{1 g}$$\sqrt{2 \mathrm{rg}}$$2 \sqrt{\mathrm{rg}}$$\sqrt{\frac{\mathrm{rg}}{2}}$Correct Option: 1 Solution: $\mathrm{r}=\frac{\ell}{\sqrt{2}}$ $\sin \theta=\frac{\mathrm{r}}{\ell}=\frac{1}{\sqrt{2}}$ $\theta=45^{\circ}$ $T \sin \theta=\frac{m v^{2}}{r}$ $\mathrm{T} \cos...
Read More →An infinite number of point charges,
Question: An infinite number of point charges, each carrying $1 \mu \mathrm{C}$ charge, are placed along the $y$-axis at $\mathrm{y}=1 \mathrm{~m}, 2 \mathrm{~m}, 4 \mathrm{~m}, 8 \mathrm{~m}$............... The total force on a $1 \mathrm{C}$ point charge, placed at the origin, is $x \times 10^{3} \mathrm{~N}$. The value of $x$, to the nearest integer, is________. [Take $\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right]$ Solution: $\mathrm{F}=\mathrm{k}(...
Read More →The radius of a sphere is measured to be
Question: The radius of a sphere is measured to be $(7.50 \pm 0.85) \mathrm{cm}$. Suppose the percentage error in its volume is $x$. The value of $x$, to the nearest $x$, is__________. Solution: $\because \mathrm{v}=\frac{4}{3} \pi \mathrm{r}^{3}$ taking $\log \$ then differentiate $\frac{\mathrm{dV}}{\mathrm{V}}=3 \frac{\mathrm{dr}}{\mathrm{r}}$ $=\frac{3 \times 0.85}{7.5} \times 100 \%=34 \%$...
Read More →For a transistor
Question: For a transistor $\alpha$ and $\beta$ are given as $\alpha=\frac{I_{C}}{I_{E}}$ and $\beta=\frac{I_{C}}{I_{B}} .$ Then the correct relation between $\alpha$ and $\beta$ will be :$\alpha=\frac{1-\beta}{\beta}$$\beta=\frac{\alpha}{1-\alpha}$$\alpha \beta=1$$\alpha=\frac{\beta}{1-\beta}$Correct Option: , 2 Solution: $\alpha=\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{E}}}, \beta=\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{B}}} ; \mathrm{I}_{\mathrm{E}}=\mathrm{I}_{\mathrm{C}...
Read More →Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.
Question: Calculate the time interval between $33 \%$ decay and $67 \%$ decay if half-life of a substance is 20 minutes.60 minutes20 minutes40 minutes13 minutesCorrect Option: 2, Solution: $\mathrm{N}_{1}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}_{1}}$ $\frac{\mathrm{N}_{1}}{\mathrm{~N}_{0}}=\mathrm{e}^{-\lambda \mathrm{t}_{1}}$ $0.67=\mathrm{e}^{-\lambda t_{1}}$ $\ln (0.67)=-\lambda t_{1}$ $\mathrm{N}_{2}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}_{2}}$ $\frac{\mathrm{N}_{2}}{\mathrm{~...
Read More →The de-Broglie wavelength of a particle having kinetic energy
Question: The de-Broglie wavelength of a particle having kinetic energy $\mathrm{E}$ is $\lambda$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to $75 \%$ of the initial value ? $\frac{1}{9} \mathrm{E}$$\frac{7}{9} \mathrm{E}$$\mathrm{E}$$\frac{16}{9} \mathrm{E}$Correct Option: , 2 Solution: $\lambda=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}, \mathrm{mv}=\sqrt{2 \mathrm{mE}}$ $\lambda \propto \frac{1}{\sqrt{E}}$ $\fra...
Read More →A TV transmission tower antenna is at a height
Question: A TV transmission tower antenna is at a height of $20 \mathrm{~m}$. Suppose that the receiving antenna is at. (i) ground level (ii) a height of $5 \mathrm{~m}$. The increase in antenna range in case (ii) relative to case (i) is $\mathbf{n} \%$. The value of $n$, to the nearest integer, is . Solution: Range $=\sqrt{2 \mathrm{Rh}}$ Range (i) $=\sqrt{2 \mathrm{Rh}}$ Range (ii) $=\sqrt{2 \mathrm{Rh}}+\sqrt{2 \mathrm{Rh}^{\prime}}$ where $h=20 \mathrm{~m} \ \mathrm{~h}^{\prime}=5 \mathrm{~m...
Read More →The boxes of masses
Question: The boxes of masses $2 \mathrm{~kg}$ and $8 \mathrm{~kg}$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8 \mathrm{~kg}$ to strike the ground starting from rest. (use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ ) $0.34 \mathrm{~s}$$0.2 \mathrm{~s}$$0.25 \mathrm{~s}$$0.4 \mathrm{~s}$Correct Option: , 4 Solution: $\left(m_{1} g-2 T\right)=m_{1} a-(1)$ $\mathrm{T}-\mathrm{m}_{2} \mathrm{~g}=\mathrm{m}_{2}(2 \mathrm{a})$ $2 \mathrm...
Read More →Consider a water tank as shown in the figure.
Question: Consider a water tank as shown in the figure. It's cross-sectional area is $0.4 \mathrm{~m}^{2}$. The tank has an opening $B$ near the bottom whose crosssection area is $1 \mathrm{~cm}^{2}$. A load of $24 \mathrm{~kg}$ is applied on the water at the top when the height of the water level is $40 \mathrm{~cm}$ above the bottom, the velocity of water coming out the opening $B$ is $\mathrm{v} \mathrm{ms}^{-1}$. The value of $\mathrm{v}$, to the nearest integer, is____________. [Take value ...
Read More →The temperature of equal masses of three different liquids
Question: The temperature of equal masses of three different liquids $\mathrm{x}, \mathrm{y}$ and $\mathrm{z}$ are $10^{\circ} \mathrm{C}, 20^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$ respectively. The temperature of mixture when $x$ is mixed with $y$ is $16^{\circ} \mathrm{C}$ and that when $\mathrm{y}$ is mixed with $\mathrm{z}$ is $26^{\circ} \mathrm{C}$. The temperature of mixture when $\mathrm{x}$ and $\mathrm{z}$ are mixed will be : $28.32^{\circ} \mathrm{C}$$25.62^{\circ} \mathrm{C}...
Read More →Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time.
Question: Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass $=500 \mathrm{~g}$, Decay constant $=20 \mathrm{~g} / \mathrm{s}$ then how much time is required for the amplitude of the system to dropAmplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass $=500 \mathrm{~g}$, Decay constant $=20 \mathrm{~g} / \mathrm{s}$ then how much time is required for the amplitude of the system to drop to ha...
Read More →Curved surfaces of a plano
Question: Curved surfaces of a plano-convex lens of refractive index $\mu_{1}$ and a plano-concave lens of refractive index $\mu_{2}$ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses. $\frac{1}{\mu_{2}-\mu_{1}}$$\mu_{1}-\mu_{2}$$\frac{1}{\mu_{1}-\mu_{2}}$$\mu_{2}-\mu_{1}$Correct Option: , 2 Solution: $\frac{1}{f_{1}}=\left(\mu_{1}-1\right)\left(\frac{1}{R}\right)$ $\frac{1}{f_{2}}=\left(\mu_{2}-1\right)\left(-\fra...
Read More →The typical output characteristics curve for a transistor
Question: The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure. The estimated current gain from the figure is Solution: $\beta=\frac{\Delta \mathrm{I}_{\mathrm{C}}}{\Delta \mathrm{I}_{\mathrm{B}}}=\frac{2 \times 10^{-3}}{10 \times 10^{-6}}$ $\beta=\frac{1}{5} \times 10^{3}$ $\beta=2 \times 10^{2}$ $\beta=200$...
Read More →A transmitting antenna
Question: A transmitting antenna has a height of $320 \mathrm{~m}$ and that of receiving antenna is $2000 \mathrm{~m}$. The maximum distance between them for satisfactory communication in line of sight mode is 'd'. The value of 'd' is ........ km. Solution: $\mathrm{d}_{\mathrm{m}}=\sqrt{2 \mathrm{Rh}_{\mathrm{T}}}+\sqrt{2 \mathrm{Rh}_{\mathrm{R}}}$ $\mathrm{d}_{\mathrm{m}}=\left(\sqrt{2 \times 6400 \times 10^{3} \times 320}+\sqrt{2 \times 6400 \times 10^{3} \times 2000}\right) \mathrm{m}$ $\mat...
Read More →A ball of mass 4kg, moving with a velocity of
Question: A ball of mass $4 \mathrm{~kg}$, moving with a velocity of $10 \mathrm{~ms}^{-1}$, collides with a spring of length $8 \mathrm{~m}$ and force constant $100 \mathrm{Nm}^{-1}$. The length of the compressed spring is $x \mathrm{~m}$. The value of $x$, to the nearest integer, is______. Solution: Let's say the compression in the spring by : y. So, by work energy theorem we have $\Rightarrow \frac{1}{2} \mathrm{mv}=\frac{1}{2} \mathrm{ky}^{2}$ $\Rightarrow y=\sqrt{\frac{m}{k}} \cdot v$ $\Rig...
Read More →Two persons A and B
Question: Two persons $A$ and $B$ perform same amount of work in moving a body through a certain distance d with application of forces acting at angle $45^{\circ}$ and $60^{\circ}$ with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person $B$ is $\frac{1}{\sqrt{x}}$. The value of $x$ is ........ Solution: Given $\mathrm{W}_{\mathrm{A}}=\mathrm{W}_{\mathrm{B}}$ $\mathrm{F}_{\mathrm{A}} \mathrm{d} \cos 45^{\circ}=\mathrm{F}_{\mathrm{B}} ...
Read More →The magnetic field in a region is given by
Question: The magnetic field in a region is given by $\overrightarrow{\mathrm{B}}=\mathrm{B}_{0}\left(\frac{\mathrm{x}}{\mathrm{a}}\right) \hat{\mathrm{k}} .$ A square loop of side $\mathrm{d}$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\overrightarrow{\mathrm{v}}=\mathrm{v}_{0} \hat{\mathrm{i}}$. The emf induced in the loop is : $\frac{\mathrm{B}_{0} \mathrm{v}_{0}^{2} \mathrm{~d}}{2 \mathrm{a}}$$\frac{\mathrm{B}_{0} \mathrm{v}_{0} \mathrm{~...
Read More →A rod CD of thermal resistance
Question: A rod CD of thermal resistance $10.0 \mathrm{KW}^{-1}$ is joined at the middle of an identical rod $A B$ as shown in figure, The end $A, B$ and $D$ are maintained at $200^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}$ and $125^{\circ} \mathrm{C}$ respectively. The heat current in CD is $\mathrm{P}$ watt. The value of $\mathrm{P}$ is ....... Solution: Rods are identical so $R_{A B}=R_{C D}=10 \mathrm{Kw}^{-1}$ $C$ is mid-point of $A B$, so $\mathrm{R}_{\mathrm{AC}}=\mathrm{R}_{\mathrm{CB}}...
Read More →The projectile motion of a particle of mass
Question: The projectile motion of a particle of mass $5 \mathrm{~g}$ is shown in the figure. The initial velocity of the particle is $5 \sqrt{2} \mathrm{~ms}^{-1}$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x \times 10^{-2} \mathrm{kgms}^{-1}$. The value of $\mathrm{x}$, to the nearest integer, is_______. Solution: $|\overrightarrow{\mathrm{u}}|=|\overrightarrow{\mathrm{v}}|$ $\ldots(1)$ $\overrightarrow{\mathrm...
Read More →If the velocity of a body
Question: If the velocity of a body related to displacement $x$ is given by $v=\sqrt{5000+24 x} \mathrm{~m} / \mathrm{s}$, then the acceleration of the body is $\ldots \ldots \mathrm{m} / \mathrm{s}^{2}$. Solution: $V=\sqrt{5000+24 x}$ $\frac{\mathrm{dV}}{\mathrm{dx}}=\frac{1}{2 \sqrt{5000+24 x}} \times 24=\frac{12}{\sqrt{5000+24 x}}$ $\operatorname{now} a=V \frac{d V}{d x}$ $=\sqrt{5000+24 x} \times \frac{12}{\sqrt{5000+24 x}}$ $\mathrm{a}=12 \mathrm{~m} / \mathrm{s}^{2}$...
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