Which one of the following graphs represents the variation of maximum kinetic energy \((E_k)\) of the emitted electrons with frequency \(\nu\) in photoelectric effect correctly?  

1. 2.
3. 4.

Subtopic:  Einstein's Photoelectric Equation |
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A vessel of height \(2~d\) is half filled with a liquid of refractive index \(\sqrt2\) and the other half with a liquid of refractive index \(n\) (the given liquids are immiscible). Then, the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be:
1. \(\frac{n}{d(n+\sqrt{2})}\)
2. \(\frac{d(n+\sqrt{2})}{n \sqrt{2}}\)
3. \(\frac{\sqrt{2} n}{d(n+\sqrt{2})}\)
4. \(\frac{n d}{d+\sqrt{2} n}\)

 

Subtopic:  Refraction at Plane Surface |
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A shell of mass \(20\) kg at rest explodes into two fragments whose masses are in the ratio \(2:3.\) The smaller fragment moves with a velocity of \(6\) m/s. The kinetic energy of the larger fragment is:
1. \(96\) J
2. \(216\) J
3. \(144\) J
4. \(360\) J

Subtopic:  Collisions |
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An electric bulb has a rated power of \(50\) W at \(100\) V. If it is used on an AC source \(200\) V, \(50\) Hz, a choke has to be used in series with it. This choke should have an inductance of:
1. \(0.1\) mH
2. \(1\) mH
3. \(0.1\) H
4. \(1.1\) H

Subtopic:  Self - Inductance |
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In Young's double slit experiment with sodium vapour lamp of wavelength \(589\) nm and the slits \(0.589\) mm apart, the half angular width of the central maximum is:
1. \(sin^{-1} (0.01)\)
2. \(sin^{-1} (0.0001)\)
3. \(sin^{-1} (0.001)\)
4. \(sin^{-1} (0.1)\)

Subtopic:  Young's Double Slit Experiment |
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A parallel plate capacitor with air as the dielectric has capacitance \(C.\) A slab of dielectric constant \(K\) having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be: 
        
1. \((K+3)\frac C4\)
2. \((K+2)\frac C4\)
3. \((K+1)\frac C4\)
4. \(\frac{KC}{4}\)

 

Subtopic:  Dielectrics in Capacitors |
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Three concurrent co-planar forces \(1\) N, \(2\) N and \(3\) N acting along different directions on a body.
Choose the correct statement:

1. can keep the body in equilibrium if \(2\) N and \(3\) N act at right angle.
2. can keep the body in equilibrium if \(1\) N and \(2\) N act at right angle.
3. cannot keep the body in equilibrium.
4. can keep the body in equilibrium in \(1\) N and \(3\) N acts at an acute angle.

Subtopic:  Resultant of Vectors |
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The work done by force acting on a body is as shown in the graph. The total work done in covering an initial distance of \(20\) m is: 
        
1. \(212.5\) J
2. \(200\) J
3. \(400\) J
4. \(175\) J

Subtopic:  Work Done by Variable Force |
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Horizontal tube of non-uniform cross-section has radii of \(0.1\) m and \(0.05\) m respectively at M and N. For a streamlined flow of the liquid, the rate of liquid flow is:
       
 

1. changing continuously with time
2. greater at M than at N
3. greater at N than at M
4. same at M and N
Subtopic:  Equation of Continuity |
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A coil of \(n\) number of turns is wound tightly in the form of a spiral with inner and outer radii \(a\) and \(b\) respectively. When a current of strength \(I\) am passed through the coil, the magnetic field at its centre is:
1. \(\frac{\mu_{_0}nI}{(b-a)}\log_e\frac ab\)
2. \(\frac{\mu_{_0}nI}{2(b-a)}\)
3. \(\frac{\mu_{_0}nI}{b}\)
4. \(\frac{\mu_{_0}nI}{2(b-a)}\log_e\frac ba\)

 

Subtopic:  Magnetic Field due to various cases |
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