1 Motion of System of Particles and Rigid Body
A Uniform chain of length L and mass M is laying on a smooth table and ½ of its length is having down over the edge of the table. If g is the acceleration due to gravity, the work done to pull the hanging part on the table is: 1) mgL/18 2) mgL/8 3) mgL/9 4) mgL/32
2 Work Energy and Power
As an object falls freely, the kinetic energy of the object 1) decreases 2) increases 3) remains the same 4) none
The kinetic energy is related to the velocity, KE=1/2mv2. As an object falls freely the velocity increases and therefore the kinetic energy increases.
3 Alternating Currents
An ideal inductor is in turn put across 220 V. 50 Hz and 220 V, 100 Hz supplies. The current flowing through it in the two cases will be then 1) equal 2) different 3) zero 4) infinite
The current in the inductor coil is given by $$I \, = \, \dfrac{V}{X_L} \, = \, \dfrac{V}{2\pi \upsilon L}$$ Since frequency $$\upsilon$$ in the two cases is different, hence the current in two cases will be different.
4 Current Electricity
A galvanometer with a coil resistance of 100 Ω gives a full scale deflection when a current of 1 mA is passed through it. The resistance of the shunt needed in ohm to convert this galvanometer into an ammeter of range 10 A is nearly 1) 0.01 2) 0.001 3) 0.1 4) 0.099
5 Motion of System of Particles and Rigid Body
A 6000 kg rocket is set for vertical firing. The exhaust speed is 900 m//s. To give an upward acceleration of 20 m/s2 the amount of gas ejected per second to supply the needed thrust is (Take g=10m/s2).
1) 225 kgs−1 2) 200 kgs−1 3) 275 kgs−1 4) 100 kgs−1
Given, $$m=6000$$kg $$v=900m/s$$ $$a=20m/s^2$$ $$\displaystyle\frac{dm}{dt}=?$$ Here, upward thrust $$=F_{th}=\displaystyle\frac{dm}{dt}v$$ Also, $$m(g+a)=F_{th}=v\displaystyle\frac{dm}{dt}$$ $$\therefore \displaystyle\frac{dm}{dt}=\frac{m(g+a)}{v}$$ $$=\displaystyle\frac{6000(10+20)}{900}$$ $$=\displaystyle\frac{60\times 30}{9}$$ $$=20\times 10$$ $$\therefore \displaystyle\frac{dm}{dt}=200kg/s$$.
6 Thermodynamics
A kettle with 2 litre waters at 27ºC is heated by operating coil heater of power 1 kW. The heat is lost to the atmosphere at constant rate 160 J/sec when its lid is open. In how much time will water is heated to 77ºC (Sp heat of H2O = 4.2 kJ.mole ) (1)8 min 20 sec (2) 6 min 2 sec (3) 14 min (4) 7 min
(1)8 min 20 sec (2) 6 min 2 sec (3) 14 min (4) 7 min
7 Physical world and measurement
A wire has a mass 0.3 ± 0.003 g, radius 0.5 ± 0.005 mm and length 6 ± 0.06 cm. The maximum percentage error in the measurement of its density is
1) 1
2) 2
3) 3
4) 4
Solution
=0.01 + 0.02 + 0.01 = 0.04
8 Gravitation
Radius of the Earth were increased by a factor of 3 and its mass remained the same, then the acceleration due to gravity on the Earth would 1) reduce by a factor of 3 2) reduce by a factor of 9 3) increase by a factor of 3 4) increase by a factor of 9
The acceleration due to gravity can be expressed as g = GM/R2 If the mass Mof the Earth remains constant and the radius R were increased by a factor of 3, then the acceleration g would reduce by a factor of 9 .
9 Wave Optics
A glass of refractive index 1.5 is coated with a thin layer of thickness of tt of refractive index 1.8 light of wavelength λ tavelling at the upper and the lower surfaes of the layer and the two reflected rays interfere. If λ=648nm , obtain the least value of tt (in 10−8m) for which the rays interfere constructively.
1) 1.8 ×10−8m
2) 0.9 ×10−8m
3) 9×10−8m
4) 18×10−8m
For constructive Interference:
10 Kinetic Theory of gases
An ideal gas has a volume of 3 l at 2 atom pressure. Keeping the temperature constant, the pressure is doubled. Then the volume of the gas will be:
(1) 1.5 l (2) any value (3) 3 l (4) 6 l
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