A fully charged capacitor has a capacitance $$C$$. It is discharged through a small coil of resistance wire, embedded in a block of specific heat $$s$$ and mass $$m$$ under thermally isolated conditions. If the temperature of the block is raised by $$\displaystyle \Delta T$$, the potential difference $$V$$ across the capacitor initially is: 

1) $$\displaystyle { \left( \frac { 2ms\Delta T }{ C } \right) }^{ 2 }$$

2) $$\displaystyle { \left( \frac { 2ms\Delta T }{ C } \right) }^{ 1/2 }$$

3) $$\displaystyle { \left( \frac { 2ms\Delta T }{ C } \right) }$$

4) $$\displaystyle 2ms\Delta TC$$

 The initial activity of a sample is measured to be 3400 decays/seconds. After 145 seconds the decay rate is measured to be 150 decays/seconds. The half-life of the sample is approximately:

(1) 2 seconds.

(2) 6 seconds.

(3)  32 seconds..

(4) 27 seconds.

A vessel of volume 0.2m³ contains hydrogen gas at temperature 300K and pressure 1bar1bar. Find the heat (in kcal) required to raise the temperature to 400K. The molar heat capacity of hydrogen at constant volume is (5 cal/molK)

1) 4
2) 2
3) 1
4) 8

 A figure skater has a moment of inertia of 4.0 kg.m² with her arms outstretched. If she begins spin at 3.0 rad/s with her arms outstretched and then brings her arms in tight to her body, her of spin increases to 7.0 rad/s in 2.5 seconds. As the skater brings her arms in tight to her body, what torque is applied to increase her spin.

1) 2.7 N.m

2) 4.0 N.m

3) 5.3 N.m

4) no torque is applied to increase her spin

A cube of aluminum has side length 0.10 m. It is dropped into a deep swimming pool of water with density 1.00 x 10³ kg/m³ . The cube comes gently to rest at the bottom of the pool. If the density of the aluminum is 2.7 x 10³  kg/m3 , the magnitude of the buoyant force acting on the aluminum is:

1) 26.6 N
2) 9.8 N
3) 2.7 N
4) 1.0 N

The equation of a simple harmonic wave is given by y=6sin2π(2t−0.1x), where x and y are in mm and t is in seconds. The phase difference between two particles 2mm apart at any instant is

1) 18^o
2) 36^o
3) 54^o
4) 72^o

 If light ray is reflected from the denser medium, the path difference produced in the reflected ray will be :

(1) λ/4

(2) λ/2

(3) λ

(4) zero

A parallel plate capacitor of capacitance C is charged and disconnected from the battery. The energy stored in it is E. If a dielectric slab of dielectric constant 6 is inserted between the plates of the capacitor then energy and capacitance will become :

1) 6E, 6C

2) E, C

3) $$\dfrac {E}{6},6C$$

4) E, 6C

A phenomenon of super conductivity has been observed at 95 K. This temperature is nearly equal to:
1.178°C
2. - 288°F
3. - 146°C
4. - 288°C

 A 100 kg person stands on a scale in an elevator. What does the scale read when the elevator is accelerating upward at 1.0 m/s².

1) 110N  

2) 900N

3) -100N

4) 1100N