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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 8601. |
An open knife edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is [BHU 2002] |
| A. | \[mg\] |
| B. | \[mg\left( 1-\frac{h}{d} \right)\] |
| C. | \[mg\left( 1+\frac{h}{d} \right)\] |
| D. | \[mg{{\left( 1+\frac{h}{d} \right)}^{2}}\] |
| Answer» D. \[mg{{\left( 1+\frac{h}{d} \right)}^{2}}\] | |
| 8602. |
In the relation \[P=\frac{\alpha }{\beta }{{e}^{-\frac{\alpha Z}{k\theta }}}\] P is pressure, Z is the distance, k is Boltzmann constant and q is the temperature. The dimensional formula of b will be [IIT (Screening) 2004] |
| A. | \[[{{M}^{0}}{{L}^{2}}{{T}^{0}}]\] |
| B. | \[[{{M}^{1}}{{L}^{2}}{{T}^{1}}]\] |
| C. | \[[{{M}^{1}}{{L}^{0}}{{T}^{-1}}]\] |
| D. | \[[{{M}^{0}}{{L}^{2}}{{T}^{-1}}]\] |
| Answer» B. \[[{{M}^{1}}{{L}^{2}}{{T}^{1}}]\] | |
| 8603. |
When one of the slits of Young?s experiment is covered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe [KCET 2002] |
| A. | 3.8 mm |
| B. | 1.6 mm |
| C. | 7.6 mm |
| D. | 3.2 mm |
| Answer» E. | |
| 8604. |
The audio signal used to modulate 60 sin (2p ´ 106 t) is \[15\sin 300\pi t.\]The depth of modulation is |
| A. | 50% |
| B. | 40% |
| C. | 25% |
| D. | 15% |
| Answer» D. 15% | |
| 8605. |
For a transistor amplifier in common emitter configuration for load impedance of 1 kW (hfe = 50 and hoe = 25 mA/V) the current gain is [AIEEE 2004] |
| A. | ? 5.2 |
| B. | ? 15.7 |
| C. | ? 24.8 |
| D. | ? 48.78 |
| Answer» E. | |
| 8606. |
In a hypothetical Bohr hydrogen, the mass of the electron is doubled. The energy \[{{E}_{0}}\]and the radius \[{{r}_{0}}\]of the first orbit will be (\[{{a}_{0}}\]is the Bohr radius) [Roorkee 1992] |
| A. | \[{{E}_{0}}=-\ 27.2\ eV;\ {{r}_{0}}={{a}_{0}}/2\] |
| B. | \[{{E}_{0}}=-\ 27.2\ eV;\ {{r}_{0}}={{a}_{0}}\] |
| C. | \[{{E}_{0}}=-13.6\ eV;\ {{r}_{0}}={{a}_{0}}/2\] |
| D. | \[{{E}_{0}}=-13.6\ eV;\ {{r}_{0}}={{a}_{0}}\] |
| Answer» B. \[{{E}_{0}}=-\ 27.2\ eV;\ {{r}_{0}}={{a}_{0}}\] | |
| 8607. |
Ultraviolet light of wavelength 300 nm and intensity 1.0 watt/m2 falls on the surface of a photosensitive material. If 1% of the incident photons produce photoelectrons, then the number of photoelectrons emitted from an area of 1.0 cm2 of the surface is nearly [AMU 1995] |
| A. | \[9.61\times {{10}^{14}}per\ \sec \]per sec |
| B. | \[4.12\times {{10}^{13}}per\ \sec \] per sec |
| C. | \[1.51\times {{10}^{12}}per\ \sec \] per sec |
| D. | \[2.13\times {{10}^{11}}per\ \sec \] per sec |
| Answer» D. \[2.13\times {{10}^{11}}per\ \sec \] per sec | |
| 8608. |
The voltage of an ac supply varies with time \[(t)\] as \[V=120\sin 100\,\pi \,t\cos 100\pi \,t.\] The maximum voltage and frequency respectively are [MP PMT 2001; MP PET 2002] |
| A. | 120 volts, 100 Hz |
| B. | \[\frac{120}{\sqrt{2}}\] volts, 100 Hz |
| C. | 60 volts, 200 Hz |
| D. | 60 volts, 100 Hz |
| Answer» E. | |
| 8609. |
Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation \[I={{I}_{0}}\sin \omega \,t\], where \[{{I}_{0}}=10A\] and w = 100 p radian/sec. The maximum value of e.m.f. in the second coil is [CBSE PMT 1998; Pb. PMT 2000] |
| A. | 2p |
| B. | 5p |
| C. | p |
| D. | 4p |
| Answer» C. p | |
| 8610. |
The dipole moment of each molecule of a paramagnetic gas is 1.5 ´ 10?23 amp ´ m2. The temperature of gas is 27oC and the number of molecules per unit volume in it is 2 ´ 1026 m?3. The maximum possible intensity of magnetisation in the gas will be |
| A. | 3 ´ 103 amp/m |
| B. | 4 ´ 10?3 amp/m |
| C. | 5 ´ 105 amp/m |
| D. | 6 ´ 10?4 amp/m |
| Answer» B. 4 ´ 10?3 amp/m | |
| 8611. |
If a wire of resistance \[20\,\Omega \] is covered with ice and a voltage of 210 V is applied across the wire, then the rate of melting of ice is [AFMC 1997] |
| A. | \[0.85\,g/s\] |
| B. | \[1.92\,g/s\] |
| C. | \[6.56\,g/s\] |
| D. | All of these |
| Answer» D. All of these | |
| 8612. |
A particle of charge +q and mass m moving under the influence of a uniform electric field \[E\hat{i}\] and a uniform magnetic field \[B\hat{k}\] follows trajectory from P to Q as shown in figure. The velocities at P and Q are \[v\hat{i}\] and \[-2v\hat{j}\] respectively. Which of the following statement(s) is/are correct [IIT 1991; BVP 2003] |
| A. | \[E=\frac{3}{4}\frac{m{{v}^{2}}}{qa}\] |
| B. | Rate of work done by electric field at P is \[\frac{3}{4}\frac{m{{v}^{3}}}{a}\] |
| C. | Rate of work done by electric field at P is zero |
| D. | Rate of work done by both the fields at Q is zero |
| Answer» C. Rate of work done by electric field at P is zero | |
| 8613. |
A sound wave of frequency n travels horizontally to the right. It is reflected from a large vertical plane surface moving to the left with a speed v. The speed of sound in the medium is c, then [IIT 1995; BCECE 2005] |
| A. | The frequency of the reflected wave is \[\frac{\nu (c+v)}{c-v}\] |
| B. | The wavelength of the reflected wave is \[\frac{c(c-v)}{\nu (c+v)}\] |
| C. | The number of waves striking the surface per second is \[\frac{\nu (c+v)}{c}\] |
| D. | The number of beats heard by a stationary listener to the left of the reflecting surface is \[\frac{\nu \ v}{c-v}\] |
| Answer» C. The number of waves striking the surface per second is \[\frac{\nu (c+v)}{c}\] | |
| 8614. |
Due to some force F1 a body oscillates with period 4/5 sec and due to other force F2 oscillates with period 3/5 sec. If both forces act simultaneously, the new period will be [RPET 1997] |
| A. | 0.72 sec |
| B. | 0.64 sec |
| C. | 0.48 sec |
| D. | 0.36 sec |
| Answer» D. 0.36 sec | |
| 8615. |
Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel (s = relative density of mercury and \[\rho \] = density of water) by |
| A. | \[\frac{{{n}^{2}}h}{{{(n+1)}^{2}}s}\] |
| B. | \[\frac{h}{({{n}^{2}}+1)\,s}\] |
| C. | \[\frac{h}{{{(n+1)}^{2}}s}\] |
| D. | \[\frac{h}{{{n}^{2}}s}\] |
| Answer» C. \[\frac{h}{{{(n+1)}^{2}}s}\] | |
| 8616. |
A piece of metal weight 46 gm in air, when it is immersed in the liquid of specific gravity 1.24 at 27ºC it weighs 30 gm. When the temperature of liquid is raised to 42ºC the metal piece weight 30.5 gm, specific gravity of the liquid at 42ºC is 1.20, then the linear expansion of the metal will be [BHU 1995] |
| A. | 3.316 × 10?5/ºC |
| B. | 2.316 × 10?5/ºC |
| C. | 4.316 × 10?5/ºC |
| D. | None of these |
| Answer» C. 4.316 × 10?5/ºC | |
| 8617. |
In the circuit shown, the value of each resistance is r, then equivalent resistance of circuit between points A and B will be [Similar to CBSE PMT 1999; RPET 1999] |
| A. | (4/3) r |
| B. | 3r / 2 |
| C. | r / 3 |
| D. | 8r / 7 |
| Answer» E. | |
| 8618. |
The vectors from origin to the points A and B are \[\overrightarrow{A}=3\hat{i}-6\hat{j}+2\hat{k}\] and \[\overrightarrow{B}=2\hat{i}+\hat{j}-2\hat{k}\] respectively. The area of the triangle OAB be |
| A. | \[\frac{5}{2}\sqrt{17}\] sq.unit |
| B. | \[\frac{2}{5}\sqrt{17}\] sq.unit |
| C. | \[\frac{3}{5}\sqrt{17}\] sq.unit |
| D. | \[\frac{5}{3}\sqrt{17}\] sq.unit |
| Answer» B. \[\frac{2}{5}\sqrt{17}\] sq.unit | |
| 8619. |
A charge \[+q\] is fixed at each of the points \[x={{x}_{0}},\,x=3{{x}_{0}},\,x=5{{x}_{0}}\]..... infinite, on the \[x-\]axis and a charge \[-q\] is fixed at each of the points \[x=2{{x}_{0}},\,x=4{{x}_{0}},x=6{{x}_{0}}\],..... infinite. Here \[{{x}_{0}}\] is a positive constant. Take the electric potential at a point due to a charge \[Q\] at a distance \[r\] from it to be \[Q/(4\pi {{\varepsilon }_{0}}r)\]. Then, the potential at the origin due to the above system of charges is [IIT 1998] |
| A. | 0 |
| B. | \[\frac{q}{8\pi {{\varepsilon }_{0}}{{x}_{0}}\ln 2}\] |
| C. | \[\infty \] |
| D. | \[\frac{q\ln 2}{4\pi {{\varepsilon }_{0}}{{x}_{0}}}\] |
| Answer» E. | |
| 8620. |
A body of mass m is taken from earth surface to the height h equal to radius of earth, the increase in potential energy will be [NCERT 1971; CPMT 1971, 97; IIT 1983; CBSE PMT 1991; Kurukshetra CEE 1996; CMEET Bihar 1995; MNR 1998; AIEEE 2004] |
| A. | mgR |
| B. | \[\frac{1}{2}mgR\] |
| C. | 2 mgR |
| D. | \[\frac{1}{4}mgR\] |
| Answer» C. 2 mgR | |
| 8621. |
The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to [CBSE PMT 1994] |
| A. | \[\sqrt{m}\] |
| B. | Independent of m |
| C. | \[1/\sqrt{m}\] |
| D. | m |
| Answer» C. \[1/\sqrt{m}\] | |
| 8622. |
\[X=3Y{{Z}^{2}}\] find dimension of \[Y\] in (MKSA) system, if \[X\] and \[Z\] are the dimension of capacity and magnetic field respectively [MP PMT 2003] |
| A. | \[{{M}^{-3}}{{L}^{-2}}{{T}^{-4}}{{A}^{-1}}\] |
| B. | \[M{{L}^{-2}}\] |
| C. | \[{{M}^{-3}}{{L}^{-2}}{{T}^{4}}{{A}^{4}}\] |
| D. | \[{{M}^{-3}}{{L}^{-2}}{{T}^{8}}{{A}^{4}}\] |
| Answer» E. | |
| 8623. |
In Young's double slit experiment, the intensity on the screen at a point where path difference is l is K. What will be the intensity at the point where path difference is \[\lambda /4\] [RPET 1996] |
| A. | \[\frac{K}{4}\] |
| B. | \[\frac{K}{2}\] |
| C. | K |
| D. | Zero |
| Answer» C. K | |
| 8624. |
One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face, forms an image 12 cm behind the silvered face. The refractive index of the glass is [CPMT 1999] |
| A. | 0.4 |
| B. | 0.8 |
| C. | 1.2 |
| D. | 1.6 |
| Answer» D. 1.6 | |
| 8625. |
A rectangular glass slab ABCD, of refractive index n1, is immersed in water of refractive index n2 (n1>n2). A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD is given by [IIT-JEE (Screening) 2000] |
| A. | \[{{\sin }^{-1}}\left[ \frac{{{n}_{1}}}{{{n}_{2}}}\cos \left( {{\sin }^{-1}}\frac{{{n}_{2}}}{{{n}_{1}}} \right) \right]\] |
| B. | \[{{\sin }^{-1}}\left[ {{n}_{1}}\cos \left( {{\sin }^{-1}}\frac{1}{{{n}_{2}}} \right) \right]\] |
| C. | \[{{\sin }^{-1}}\left( \frac{{{n}_{1}}}{{{n}_{2}}} \right)\] |
| D. | \[{{\sin }^{-1}}\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)\] |
| Answer» B. \[{{\sin }^{-1}}\left[ {{n}_{1}}\cos \left( {{\sin }^{-1}}\frac{1}{{{n}_{2}}} \right) \right]\] | |
| 8626. |
A glass hemisphere of radius 0.04 m and R.I. of the material 1.6 is placed centrally over a cross mark on a paper (i) with the flat face; (ii) with the curved face in contact with the paper. In each case the cross mark is viewed directly from above. The position of the images will be [ISM Dhanbad 1994] |
| A. | (i) 0.04 m from the flat face; (ii) 0.025 m from the flat face |
| B. | (i) At the same position of the cross mark; (ii) 0.025 m below the flat face |
| C. | (i) 0.025 m from the flat face; (ii) 0.04 m from the flat face |
| D. | For both (i) and (ii) 0.025 m from the highest point of the hemisphere |
| Answer» C. (i) 0.025 m from the flat face; (ii) 0.04 m from the flat face | |
| 8627. |
The diode used in the circuit shown in the figure has a constant voltage drop of 0.5 V at all currents and a maximum power rating of 100 milliwatts. What should be the value of the resistor R, connected in series with the diode for obtaining maximum current [CBSE PMT 1997] |
| A. | 1.5 W |
| B. | 5 W |
| C. | 6.67 W |
| D. | 200 W |
| Answer» C. 6.67 W | |
| 8628. |
A 500 Hz modulating voltage fed into an FM generator produces a frequency deviation of 2.25 kHz. If amplitude of the voltage is kept constant but frequency is raised to 6 kHz then the new deviation will be |
| A. | 4.5 kHz |
| B. | 54 kHz |
| C. | 27 kHz |
| D. | 15 kHz |
| Answer» C. 27 kHz | |
| 8629. |
\[\alpha -\]particles of energy 400 KeV are bombarded on nucleus of\[_{82}Pb\]. In scattering of \[\alpha -\]particles, its minimum distance from nucleus will be [RPET 1997] |
| A. | 0.59 nm |
| B. | 0.59 Å |
| C. | 5.9 pm |
| D. | 0.59 pm |
| Answer» E. | |
| 8630. |
In a photoemissive cell with executing wavelength \[\lambda \], the fastest electron has speed v. If the exciting wavelength is changed to \[3\lambda /4\], the speed of the fastest emitted electron will be [CBSE PMT 1998] |
| A. | \[v\ {{(3/4)}^{1/2}}\] |
| B. | \[v\ {{(4/3)}^{1/2}}\] |
| C. | Less than \[v\ {{(4/3)}^{1/2}}\] |
| D. | Greater than \[v\ {{(4/3)}^{1/2}}\] |
| Answer» E. | |
| 8631. |
In the circuit shown in figure neglecting source resistance the voltmeter and ammeter reading will respectively, will be [KCET (Engg.) 2001] |
| A. | 0V, 3A |
| B. | 150V, 3A |
| C. | 150V, 6A |
| D. | 0V, 8A |
| Answer» E. | |
| 8632. |
Two identical circular loops of metal wire are lying on a table without touching each other. Loop-A carries a current which increases with time. In response, the loop-B [IIT JEE 1999; UPSEAT 2003] |
| A. | Remains stationary |
| B. | Is attracted by the loop-A |
| C. | Is repelled by the loop-A |
| D. | Rotates about its CM, with CM fixed (CM is the centre of mass) |
| Answer» D. Rotates about its CM, with CM fixed (CM is the centre of mass) | |
| 8633. |
Two magnets of equal mass are joined at right angles to each other as shown the magnet 1 has a magnetic moment 3 times that of magnet 2. This arrangement is pivoted so that it is free to rotate in the horizontal plane. In equilibrium what angle will the magnet 1 subtend with the magnetic meridian |
| A. | \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\] |
| B. | \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\] |
| C. | \[{{\tan }^{-1}}(1)\] |
| D. | 0° |
| Answer» C. \[{{\tan }^{-1}}(1)\] | |
| 8634. |
An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from room temperature\[20{}^\circ C\]? The temperature of boiling water is \[100{}^\circ C\] [RPET 1996] |
| A. | 6.4 minutes |
| B. | 6.3 minutes |
| C. | 12.6 minutes |
| D. | 12.8 minutes |
| Answer» C. 12.6 minutes | |
| 8635. |
The difference between the apparent frequency of a source of sound as perceived by an observer during its approach and recession is 2% of the natural frequency of the source. If the velocity of sound in air is 300 m/sec, the velocity of the source is (It is given that velocity of source |
| A. | 6 m/sec |
| B. | 3 m/sec |
| C. | 1.5 m/sec |
| D. | 12 m/sec |
| Answer» C. 1.5 m/sec | |
| 8636. |
Two identical stringed instruments have frequency 100 Hz. If tension in one of them is increased by 4% and they are sounded together then the number of beats in one second is [EAMCET (Engg.) 1995] |
| A. | 1 |
| B. | 8 |
| C. | 4 |
| D. | 2 |
| Answer» E. | |
| 8637. |
A string of length 0.4 m and mass \[{{10}^{-2}}\,kg\] is tightly clamped at its ends. The tension in the string is 1.6 N. Identical wave pulses are produced at one end at equal intervals of time Dt. The minimum value of Dt which allows constructive interference between successive pulses is [IIT 1998] |
| A. | 0.05 s |
| B. | 0.10 s |
| C. | 0.20 s |
| D. | 0.40 s |
| Answer» C. 0.20 s | |
| 8638. |
A particle is performing simple harmonic motion along x-axis with amplitude 4 cm and time period 1.2 sec. The minimum time taken by the particle to move from x =2 cm to x = + 4 cm and back again is given by [AIIMS 1995] |
| A. | 0.6 sec |
| B. | 0.4 sec |
| C. | 0.3 sec |
| D. | 0.2 sec |
| Answer» C. 0.3 sec | |
| 8639. |
A large horizontal surface moves up and down in SHM with an amplitude of 1 cm. If a mass of 10 kg (which is placed on the surface) is to remain continually in contact with it, the maximum frequency of S.H.M. will be [SCRA 1994; AIIMS 1995] |
| A. | 0.5 Hz |
| B. | 1.5 Hz |
| C. | 5 Hz |
| D. | 10 Hz |
| Answer» D. 10 Hz | |
| 8640. |
A U tube of uniform bore of cross-sectional area A has been set up vertically with open ends facing up. Now m gm of a liquid of density d is poured into it. The column of liquid in this tube will oscillate with a period T such that |
| A. | \[T=2\pi \sqrt{\frac{M}{g}}\] |
| B. | \[T=2\pi \sqrt{\frac{MA}{gd}}\] |
| C. | \[T=2\pi \sqrt{\frac{M}{gdA}}\] |
| D. | \[T=2\pi \sqrt{\frac{M}{2Adg}}\] |
| Answer» E. | |
| 8641. |
The only possibility of heat flow in a thermos flask is through its cork which is 75 cm2 in area and 5 cm thick. Its thermal conductivity is 0.0075 cal/cmsecoC. The outside temperature is 40oC and latent heat of ice is 80 cal g?1. Time taken by 500 g of ice at 0oC in the flask to melt into water at 0oC is [CPMT 1974, 78; MNR 1983] |
| A. | 2.47 hr |
| B. | 4.27 hr |
| C. | 7.42 hr |
| D. | 4.72 hr |
| Answer» B. 4.27 hr | |
| 8642. |
Work done by a system under isothermal change from a volume \[{{V}_{1}}\] to \[{{V}_{2}}\] for a gas which obeys Vander Waal's equation \[(V-\beta n)\,\left( P+\frac{\alpha {{n}^{2}}}{V} \right)=nRT\] |
| A. | \[nRT{{\log }_{e}}\left( \frac{{{V}_{2}}-n\beta }{{{V}_{1}}-n\beta } \right)+\alpha \,{{n}^{2}}\,\left( \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}{{V}_{2}}} \right)\] |
| B. | \[nRT{{\log }_{10}}\left( \frac{{{V}_{2}}-\alpha \beta }{{{V}_{1}}-\alpha \beta } \right)+\alpha \,{{n}^{2}}\,\left( \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}{{V}_{2}}} \right)\] |
| C. | \[nRT{{\log }_{e}}\left( \frac{{{V}_{2}}-n\alpha }{{{V}_{1}}-n\alpha } \right)+\beta \,{{n}^{2}}\,\left( \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}{{V}_{2}}} \right)\] |
| D. | \[nRT{{\log }_{e}}\left( \frac{{{V}_{1}}-n\beta }{{{V}_{2}}-n\beta } \right)+\alpha \,{{n}^{2}}\,\left( \frac{{{V}_{1}}{{V}_{2}}}{{{V}_{1}}-{{V}_{2}}} \right)\] |
| Answer» B. \[nRT{{\log }_{10}}\left( \frac{{{V}_{2}}-\alpha \beta }{{{V}_{1}}-\alpha \beta } \right)+\alpha \,{{n}^{2}}\,\left( \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}{{V}_{2}}} \right)\] | |
| 8643. |
The coefficient of volumetric expansion of mercury is 18 × 10?5/ºC. A thermometer bulb has a volume 10?6 m3 and cross section of stem is 0.004 cm2. Assuming that bulb is filled with mercury at 0ºC then the length of the mercury column at 100ºC is [Pb. PMT 1998, DPMT 1997, 2001] |
| A. | 18.8 mm |
| B. | 9.2 mm |
| C. | 7.4 cm |
| D. | 4.5 cm |
| Answer» E. | |
| 8644. |
There are three resistance coils of equal resistance. The maximum number of resistances you can obtain by connecting them in any manner you choose, being free to use any number of the coils in any way is [ISM Dhanbad 1994] |
| A. | 3 |
| B. | 4 |
| C. | 6 |
| D. | 5 |
| Answer» C. 6 | |
| 8645. |
There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density \[\rho \]. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is |
| A. | \[gh\rho a\] |
| B. | \[\frac{2gh}{\rho \,a}\] |
| C. | \[2\rho agh\] |
| D. | \[\frac{\rho gh}{a}\] |
| Answer» D. \[\frac{\rho gh}{a}\] | |
| 8646. |
A force \[\overrightarrow{F}=-K(y\hat{i}+x\hat{j})\] (where K is a positive constant) acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken along the positive x- axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the forces \[\overrightarrow{F}\] on the particle is [IIT-JEE 1998] |
| A. | \[-2\,K{{a}^{2}}\] |
| B. | \[2\,K{{a}^{2}}\] |
| C. | \[-K{{a}^{2}}\] |
| D. | \[K{{a}^{2}}\] |
| Answer» D. \[K{{a}^{2}}\] | |
| 8647. |
An ellipsoidal cavity is carved within a perfect conductor. A positive charge \[q\] is placed at the centre of the cavity. The points \[A\] and \[B\] are on the cavity surface as shown in the figure. Then [IIT-JEE (Screening) 1999] |
| A. | Electric field near \[A\] in the cavity = Electric field near \[B\] in the cavity |
| B. | Charge density at \[A=\] Charge density at \[B\] |
| C. | Potential at \[A=\] Potential at \[B\] |
| D. | Total electric field flux through the surface of the cavity is \[q/{{\varepsilon }_{0}}\] |
| Answer» 3 , 4. Total electric field flux through the surface of the cavity is \[q/{{\varepsilon }_{0}}\] | |
| 8648. |
An Indian rubber cord L metre long and area of cross-section A\[metr{{e}^{2}}\] is suspended vertically. Density of rubber is D \[kg/metr{{e}^{3}}\] and Young's modulus of rubber is E \[newton/metr{{e}^{2}}\]. If the wire extends by l metre under its own weight, then extension l is |
| A. | \[{{L}^{2}}Dg/E\] |
| B. | \[{{L}^{2}}Dg/2E\] |
| C. | \[{{L}^{2}}Dg/4E\] |
| D. | L |
| Answer» C. \[{{L}^{2}}Dg/4E\] | |
| 8649. |
Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between planet and star is proportional to \[{{R}^{-\frac{5}{2}}}\], then \[{{T}^{2}}\] is proportional to [IIT 1989; RPMT 1997] |
| A. | \[{{R}^{3}}\] |
| B. | \[{{R}^{7/2}}\] |
| C. | \[{{R}^{5/2}}\] |
| D. | \[{{R}^{3/2}}\] |
| Answer» C. \[{{R}^{5/2}}\] | |
| 8650. |
A ball hits the floor and rebounds after inelastic collision. In this case [IIT 1986] |
| A. | The momentum of the ball just after the collision is the same as that just before the collision |
| B. | The mechanical energy of the ball remains the same in the collision |
| C. | The total momentum of the ball and the earth is conserved |
| D. | The total energy of the ball and the earth is conserved |
| Answer» D. The total energy of the ball and the earth is conserved | |