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Given below are two statements : Statement (I) : Dimensions of specific heat is $$[L^2 T^{-2} K^{-1}]$$. Statement (II) : Dimensions of gas constant is $$[ML^2 T^{-1} K^{-1}]$$. In the light of the above statements, choose the most appropriate answer from the options given below.
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A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $$t_1$$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $$t_2$$. Time required to reach the ground, if it is dropped from the top of the tower, is :
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A body of weight $$200 \text{ N}$$ is suspended from a tree branch through a chain of mass $$10 \text{ kg}$$. The branch pulls the chain by a force equal to (if $$g = 10 \text{ m/s}^2$$) :
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A car of $$800 \text{ kg}$$ is taking turn on a banked road of radius $$300 \text{ m}$$ and angle of banking $$30°$$. If coefficient of static friction is $$0.2$$ then the maximum speed with which car can negotiate the turn safely: $$(g = 10 \text{ m/s}^2, \sqrt{3} = 1.73)$$
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When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be:
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Assuming the earth to be a sphere of uniform mass density, a body weighed $$300 \text{ N}$$ on the surface of earth. How much it would weigh at $$R/4$$ depth under surface of earth?
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Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $$R$$ = Radius of bubble, $$S$$ = Surface tension of bubble)
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A total of $$48 \text{ J}$$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $$2°C$$. The work done by the gas is: Given, $$R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}$$.
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Energy of 10 non rigid diatomic molecules at temperature $$T$$ is :
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Two identical conducting spheres $$P$$ and $$S$$ with charge $$Q$$ on each, repel each other with a force $$16 \text{ N}$$. A third identical uncharged conducting sphere $$R$$ is successively brought in contact with the two spheres. The new force of repulsion between $$P$$ and $$S$$ is :
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The number of electrons flowing per second in the filament of a $$110 \text{ W}$$ bulb operating at $$220 \text{ V}$$ is : (Given $$e = 1.6 \times 10^{-19} \text{ C}$$)
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Match List-I with List-II :
Choose the correct answer from the options given below :
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In a coil, the current changes from $$-2 \text{ A}$$ to $$+2 \text{ A}$$ in $$0.2 \text{ s}$$ and induces an emf of $$0.1 \text{ V}$$. The self inductance of the coil is :
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In the given electromagnetic wave $$E_y = 600 \sin(\omega t - kx) \text{ Vm}^{-1}$$, intensity of the associated light beam is (in $$\text{W/m}^2$$) : (Given $$\epsilon_0 = 9 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2}$$)
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In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $$= 49$$ MSD; 20 divisions on main scale in each cm. For mark on paper MSR $$= 8.45 \text{ cm}$$, VC $$= 26$$. For mark on paper seen through slab MSR $$= 7.12 \text{ cm}$$, VC $$= 41$$. For powder particle on the top surface of the glass slab MSR $$= 4.05 \text{ cm}$$, VC $$= 1$$. (MSR = Main Scale Reading, VC = Vernier Coincidence) Refractive index of the glass slab is :
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For the thin convex lens, the radii of curvature are at $$15 \text{ cm}$$ and $$30 \text{ cm}$$ respectively. The focal length the lens is $$20 \text{ cm}$$. The refractive index of the material is :
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When UV light of wavelength $$300 \text{ nm}$$ is incident on the metal surface having work function $$2.13 \text{ eV}$$, electron emission takes place. The stopping potential is: (Given $$hc = 1240 \text{ eVnm}$$)
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The longest wavelength associated with Paschen series is : (Given $$R_H = 1.097 \times 10^7 \text{ SI unit}$$)
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The acceptor level of a p-type semiconductor is $$6 \text{ eV}$$. The maximum wavelength of light which can create a hole would be : Given $$hc = 1242 \text{ eVnm}$$.
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In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $$4^{th}$$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is $$0.04 \text{ mm}$$ then how many main scale divisions are there in $$1 \text{ cm}$$?
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A particle moves in a straight line so that its displacement $$x$$ at any time $$t$$ is given by $$x^2 = 1 + t^2$$. Its acceleration at any time $$t$$ is $$x^{-n}$$ where $$n =$$ ___________
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Three balls of masses $$2 \text{ kg}$$, $$4 \text{ kg}$$ and $$6 \text{ kg}$$ respectively are arranged at centre of the edges of an equilateral triangle of side $$2 \text{ m}$$. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ___________ $$\text{kgm}^2$$.
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A wire of cross sectional area A, modulus of elasticity $$2 \times 10^{11} \text{ Nm}^{-2}$$ and length $$2 \text{ m}$$ is stretched between two vertical rigid supports. When a mass of $$2 \text{ kg}$$ is suspended at the middle, it sags lower from its original position making an angle $$\theta = \frac{1}{100}$$ radian on the points of support. The value of A is ___________ $$\times 10^{-4} \text{ m}^2$$ (consider $$x << L$$). (given : $$g = 10 \text{ m/s}^2$$)
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Two open organ pipes of lengths $$60 \text{ cm}$$ and $$90 \text{ cm}$$ resonate at $$6^{th}$$ and $$5^{th}$$ harmonics respectively. The difference of frequencies for the given modes is ___________ Hz. (Velocity of sound in air $$= 333 \text{ m/s}$$)
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A capacitor of capacitance $$10 \mu\text{F}$$ whose plates are separated by $$10 \text{ mm}$$ through air and each plate has area $$4 \text{ cm}^2$$ is now filled equally with two dielectric media of $$K_1 = 2$$, $$K_2 = 3$$ respectively as shown in figure. If new force between the plates is $$8 \text{ N}$$. The supply voltage is ___________ $$\text{ V}$$.
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In the given figure an ammeter A consists of a $$240 \Omega$$ coil connected in parallel to a $$10 \Omega$$ shunt. The reading of the ammeter is ___________ mA.
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A coil having 100 turns, area of $$5 \times 10^{-3} \text{ m}^2$$, carrying current of $$1 \text{ mA}$$ is placed in uniform magnetic field of $$0.20 \text{ T}$$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $$90°$$ is ___________ $$\mu\text{J}$$.
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For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $$2.5 \text{ nF}$$. If resistance of $$200 \Omega$$ and $$100 \text{ mH}$$ inductor is being used in the given circuit. The frequency of ac source is ___________ $$\times 10^3 \text{ Hz}$$. (given $$\pi^2 = 10$$)
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Two coherent monochromatic light beams of intensities I and 4I are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $$xI$$. The value of $$x$$ is ___________.
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In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ___________ nm. (Given $$hc = 1245 \text{ eVnm}$$, $$e = 1.6 \times 10^{-19} \text{ C}$$).
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