Thermal questions

                                                        Questions  
                                                  

1.    Calculate the angle of (a) 1⁰ (degree) (b) 1^’ (minute of are or are min) and (c) 1^’’ (second of arc or arc sec) in radian. Use 360 = 2π rad. 1⁰=60^’ and 1^’=60’’.

2.    Which of these is largest: astronomical unit, light year and per sec?

3.    The screw of a spherometer moves by 4mm. When its circular scale is given four complete rotations. If circular scale has 200 division, calculate pitch and least count of the spherometer.

4.    In the Vander Wall’s equation    
what are the dimensions of a and b? Here, P is pressure, V is volume, T is temperature and R is gas constant.

5.    Write the dimensions of a and b in relation      
Where P is power, x is distance and t is time.

6.    The frequency of vibration (v) of a string may depend upon length (l) of the string, tension (T) in the string and mass per unit length (m) of the string. Using the method of dimensions, derive the formula for v.

7.    The centripetal force F acting on a particle moving uniformly in a circle may depend upon mass (m) and radius (r) of the circle. Derive the formula for F using the method of dimensions.

8.    Can a quantity have dimensions, but still have no units?

9.    Can a quantity have units, but still have no dimensions?

10.  Does quantity have different dimensions in different system of units?

11.  Match the physical quantities with dimensions expressed in disarray.
(i) Angular momentum                                       
(ii)Latent heat                                                    
(iii)Specific heat                                                         
(iv) Joule’s mechanical equivalent of heat     
(v) Resistivity                                                    
(vi) Gravitational constant                               

12.  Justify L + L=L and L - L=L

13.  Write the dimensions of a and b in the formula u = a + bt , where v is velocity and t is time.

14.  The diameter of a wire measured by a Screw gauge was found to be 1.328, 1.330, 1.325, 1.326, 1.334 and 1.336cm. Calculate
(i) mean value of diameter
(ii) absolute error in each measurement
(iii) Mean absolute error
(iv) fractional error
(v) percentage error
Also express the result in terms of absolute error and percentage error.

15.  We measure the period of oscillation of a simple pendulum. In successive measurements the readings are to be 2.63s, 2.36s, 2.42s, r2.71s, and 2.80s. Calculate the absolute relative error and percentage error.

16.  Add 17.35g, 25.6g; and 8.498g and write the result with the correct number of significant figures.

17.  The resistance R = V/I, Where V = (100±5) volt and I = (10±0.2)Amp . Find the percentage error in R.

18.  The resistor of resistance R₁ = 100±3 ohm and R₂ = 200±4 ohm are connected (a) in series (b) in parallel. Find the equivalent resistance of the (a) series combination (b) parallel combination.
Use for a, relation R = R₁ + R₂  and for (b)
    

19.  Calculate the percentage error I specific resistance
 ρ = πr²R/l, where
r = radius of wire = (0.26±0.02) cm
l = length of wire = (156.0±0.1)cm
R = Resistance of wire = (64±2)ohm.

20.  Which of the following length measurement is most accurate and why?
(i) 4.00 cm (ii) 0.004 mm (iii) 40.00 cm.

21.  State the number of significant figures in the following:
(a) 0.007 m².       (b) 2.64*10²⁴.     (c) 0.2371g cm-³.         (d) 6.320 J
(e) 6.032 N m^-2.  (f) 0.0006032 m².

22.  The nearest star to our solar system is 4.29 light year away. How much is this distance in terms of per sec? How much parallax would this star show when viewed from two locations of the earth six months apart in its orbit around the sun?

23.  Where the Jupiter is at a distance of 824.7 Million kilometers from the Earth. Its angular diameter is to be 35.72^’’ of arc. Calculate the diameter of Jupiter?

24.  Which of the following measurement is most accurate and which is most precise:
(i) 4.00 mm         (ii) 4.00 cm         (iii) 4.00 m          (iv) 40.00 m ?

25.  A man walks on a straight road from his home to market 3km away with a speed of 6km/hr. finding the market closed, he instantly turns and walks back with a speed of 9km/hr. What is the
(a) magnitude of average velocity
(b) average speed of the man, over the interval of time
     (i) 0 to 30 min
     (ii) 0 to 50 min
     (iii) 0 to 40 min.

26.  Delhi is at a distance of 200km form Ambala. A sets out from Ambala at a speed of 30km/hr, and B sets out at the same time from Delhi at a speed of km/hr. When they will meet each other?

27.  Can the speed of body be negative?

28.  Can displacement greater than distance travelled by an object?

29.  What will be nature of velocity-time graph for a uniform motion?

30.  What will be nature of position-time graph for a uniform motion?

31.  Is it true one dimensional motion, a particle with zero speed may have non-zero velocity?

32.  Given    and   . Find the unit vector of
(i) (                (ii) (

33.  What is angle made by vector,   with x-axis?

34.  There are two displacement vectors, on of magnitude 3m and other of 4m. How would the two vectors be added so that the magnitude of the resultant vector be
(a) 7m  (b) 1m  (c) 5m

35.  Can any of the rectangular components of a given vector have magnitude greater than the vector itself? Explain.

36.  Find the vector A and is magnitude with initial point 
P(1, 2, -1) and terminal point Q(3, 2, 2).

37.  Two tall buildings are 200m apart. With what speed must a ball be thrown horizontally form the window 540m above the ground in one building, so that it will enter a window 50m above the ground in the other?

38.  A plane flying horizontally at 100ms at a height 1000m releases a bomb from it. Find
(a) the time it takes to reach the ground
(b) The velocity with which the bomb hits the target in ground
(c) the distance of the target

39.  A fighter plane flying horizontally at an altitude of 1.5km with speed of 720km/hr. passes directly overhead an anticragt gun. At what angle from the vertical should the gun be fired from the shell with muzzle speed 400 m/s to his the plane to shortest time?

40.  A boy stands at 78.4m from a building and throws a ball which just enters a window 39.2m above the ground. Calculate the velocity of projection of the ball.

41.  The resultant of two vectors and  perpendicular to the vector  and its magnitude is equal to half of the magnitude of the vector. Find out the angle between  and .

42.  A weight mg is suspended form the middle of a rope whose ends are at the same level. The rope is no longer horizontal. Find the minimum tension required to completely straighten the rope.