CLASS 11 - ASSIGNMENT 5 - UNITS AND MEASUREMENTS - SUMS

 CLASS 11

ASSIGNMENT 5

UNITS AND MEASUREMENTS - SUMS


1. Convert an acceleration of 10m/s² in km/h².


2. The mass of a proton is 1.67 x 10 ⁻²⁷ kg.  How many protons would make 1 g?


3. The density of a material is 0.8 g cm⁻ﱣ³.  Express it in SI units.


4. What is the number of electrons that would weigh 1 kg?  Mass of an electron is 9.11 x 10⁻³¹  kg.


5. What is the order of magnitude of (i) 869000 (ii) 0.05?


6. What is the order of magnitude of seconds in a day?


7. Calculate the angle of 1 degree in radians.


8. If the units of force, energy and velocity are 20N, 200J and 5 ms⁻¹, find the units of length, mass and time.


9. Find the value of 100 J on a system which has 20 cm, 250 g and half minute as fundamental units of length, mass ad time.


10. Check whether the equation E = mc² is correct by the method of dimensions.


11. The distance covered by a particle in time t is given by x = a + bt + ct² + dt³ .  Find the dimensions of a, b, c and d.


12. Consider a simple pendulum, having a bob attached to a string that oscillates under the action of the force of gravity.  Suppose that the period of oscillation of the simple pendulum depends on (i) mass m of the bob (ii) length l of the pendulum and (iii) acceleration due to gravity g at the place.  Derive the expression for its time period using method of dimensions.


13. Find the number of significant figures in the following:

     (i) 0.3720 g cm⁻³   (ii) 7.58 x 10²⁴ kg


14. Convert 1 metre into light year.


15. The velocity of a body which has fallen freely under gravity varies as (g^p)(h^q), where g is the acceleration due to gravity at the place and h is the height through which the body has fallen.  Find the values of p and q.


16. If the velocity of light c, the constant of gravitation G and Planck's constant h be chosen as the fundamental units, find the dimensions of mass, length and time in terms of c, G and h.


17. A calorie is a unit of heat energy and it equals about 4.2 J, where 1 J = 1 kg m² s⁻²  .  Suppose we employ a system of units in which the unit of mass equals 𝛂 kg, the unit of length equals  𝞫 m, the unit of time  is  𝜸 s.  Show that a calorie has a magnitude 4.2 𝞪⁻¹ 𝞫⁻²𝞬²     in terms of the new units.


18. A vehicle is moving with a speed of 18 km/h.  Find the distance (in metres) covered in 1 second?

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