WBJEE  Physics (Category  2) Model Test
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Question 1 
A solid homogeneous cube floats at the interface of two liquids, mercury and water, kept in a container such that the lower portion of the cube is immersed in mercury and the upper portion is in water. The density of the material of the cube is 7.3 gm/cc and those of mercury and water are respectively 13.6 gm/cc and 1.0 gm/cc. Then the % of volume of the cube immersed in mercury is
A  70% 
B  68% 
C  50% 
D  73% 
Question 2 
The dimension of a quantity is given by ML^{2}T^{2} I^{2}, where M is mass, L is length, T is time, and I is electric current. Which of the following quantities has this dimension?
A  Capacitor 
B  Inductance 
C  Magnetic Flux 
D  Electric Flux 
Question 3 
A car P moves with a velocity V towards a stationary observer M. Another car Q moves away from M in the same direction with same velocity V. Both the cars continuously blow whistles of same frequency 380 Hz and the observer M hears 20 beats /sec. Assume the velocity of sound is 340 m/sec. The value of V in m/sec is
A  11.3 
B  17.0 
C  20.9 
D  8.5 
Question 4 
The same weight of mg is hung from two wires of length l, radius r, and length 2l, radius 2r respectively, having the same Young’s modulus Y. Then, the net elongation equals
A  (2mgl) / (3πr^{2}Y) 
B  (mgl) / (3πr^{2}Y) 
C  (mgl) / (2πr^{2}Y) 
D  (3mgl) / (2πr^{2}Y) 
Question 5 
A proton is at rest and is free to move . Another proton moving with a velocity V_{0} strikes the proton at rest. Denote proton mass and charge as m and e respectively and assume a headon collision. Then the closest distance the incident proton approaches towards the other proton is
A  e^{2} / (4πε_{0}mV_{0}^{2}) 
B  e^{2} / (2πε_{0}mV_{0}^{2}) 
C  e^{2} / (πε_{0}mV_{0}^{2}) 
D  2e^{2} / (4πε_{0}mV_{0}^{2}) 
Question 6 
If I is the moment of inertia and E is the kinetic energy of rotation of a body, its angular momentum will be
A  √EI 
B  2EI 
C  E / I 
D  √2EI 
Question 7 
A spherical black body of radius 12cm radiates 450W power at 500° K. If the radius is halved and temperature doubled, the power radiated in watts would be
A  225

B  450 
C  900 
D  1800 
Question 8 
An oil drop of radius 10^{6} m carries charge equal to that of 3 electrons. If density of oil is 2 x 10^{3} kg / m^{3}, the electric field required to keep the drop stationary is
A  1.71 x 10^{5} V / m

B  1.71 x 10^{3} V / m 
C  1.71 x 10^{6} V / m 
D  1.71 V / m 
Question 9 
In a Carnot heat engine, 8000 J of heat is absorbed from a source of 400° K and 6000 J of heat is rejected to sink. The temperature of the sink is
A  100° K

B  300° K 
C  0° K 
D  273° K 
Question 10 
A body cools from 50° C to 49.9° C in 5 sec. How long will it take to cool from 40° C to 39.9° C? (The temperature of the surroundings is 30° C)
A  20 sec

B  15 sec 
C  10 sec 
D  5 sec 
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