PHYSICS. Topic: Units and Dimension, Motion in straight line

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1 PHYSICS Topic: Units and Dimension, Motion in straight line 1. Check the correctness of the following equations (i) v 2 =u 2 +2aS (ii) K E=1/2 mv 2 2. Centripetal force acting on a body moving along a circular path depends on (i) mass of body (m), velocity of the body (v), radius of circular path (r). Using the method of dimensions derive the expression for centripetal force. 3. Energy of a body executing SHM depends on (i) mass of the body(m) (ii) amplitude with which the body oscillate(a) (iii)frequency of oscillation(ν) using the method of dimensions derive the expression for centripetal force. 4. Convert one Newton into dyne using the method of dimensions. 5. Assuming that the mass M of the largest stone that can be moved by a flowing river depends upon v the velocity, ρ the density of water and on g the acceleration due to gravity. Using dimensions show that M varies with the sixth power of the velocity of flow. 6. If x = a + bt + ct 2, where x is in metres, t in seconds, what is the unit of c? 7. Write the dimensional formulae of the following: Power, pressure, mass density, momentum, resistance, acceleration. 8. Find the dimensions of a and b in the equation F= at + bt 2, where F is force and t is time. 9. If 500g be the unit of mass, 50s the unit of time and acceleration due to gravity 980cms -2 be the unit of acceleration, find what will be the new unit of energy? Unit-II: Kinematics 1. A car starting from rest acquires a speed of 25ms -1 in 10 seconds, after which it maintains this speed for 10 seconds. Find (a) the acceleration (b) distance traveled during acceleration (c) total distance traveled? 2. Show that the area under velocity-time graph gives the displacement of the body? 3. A particle moves along x-axis in such a way that its coordinate (x) varies with time t, according to expression x=2-5t+6t.find the initial velocity of the particle and acceleration x in meter and t in second. 4. A particle is projected at 60º to the horizontal with a kinetic energy K. What is the kinetic energy at the highest point? 5. Which of the following statements is false for a particle moving in a circle with a constant angular speed? (a) the velocity vector is tangent to the circle (b) the acceleration vector is tangent to the circle (c) the acceleration vector points to the centre of the circle (d) the velocity and acceleration vectors are perpendicular to each other 6. If a body travels half of its path in the last second of its fall from rest; find the time and height of its fall?

2 7. A bullet strikes a uniform plank with a speed of 400ms -1 and comes out with the half the velocity. What would be the velocity if the plank were only half thick? 8. A train passes three points A,B,C at 24 kmh -1,36 kmh -1,54 kmh -1 respectively with uniform acceleration. If the distance AB=2 km, find the distance BC? 9. A stone thrown vertically up went up 98m and came down. How long it was in air? 10. A man walks on a straight road from his home to market, which is 2.5km away from his home with a speed of 5kmh -1. Finding market closed, he returns and walks back to home with a speed of 7.5kmh Find out the average speed the person? From the velocity-time graph of uniform accelerated motion deduce the equations of motion in (i) Velocity and time (ii) distance and time (iii) distance and velocity. 11. A body moving with uniform acceleration describes 20 m in 2 nd and 30 m in 4 th second of its motion. Describe the distance moved by it in 6 th second. 12. A particle is thrown vertically upwards with the velocity of 19.6 m/s.find a. the velocity and acceleration of the particle at the highest point. b. how high a particle will rise? c. time taken for rising to the highest point. d. time taken for falling from the highest point of projection. e. its velocity, when it comes back to the point of projection. 13. A rubber ball is dropped from a height of 3m. After striking the ground it rises to height of 2 m. If it remains in contact with the ground for 0.01s, find the average acceleration during this time. 14. A particle is moving along x- axis. The position of the particle at any instant is given by X = a + bt 2. Where, a = 6m and b = 3.5 m/s 2. T is measured in seconds. Find (i) the velocity of the particle at t = 0s and t = 3s. (ii) the average velocity between t = 3s and t = 6s. 15. The velocity of a particle is given by the equation, v = 2t cm/s. Find (i) the change in velocity of the particle during the time interval between t 1 = 2s and t 2 = 4s (ii) the average acceleration during the same interval and (iii) the instantaneous acceleration at t 2 = 4s. 16. A ball is thrown upwards with an initial velocity of 100 m/s. After how much time will it return? Draw velocity time graph for the ball and find from the graph (i) the maximum height attained by the ball and (ii) height of the ball after 15 s. Take g = 10 m/s A car, starting from rest, accelerates at the rate f through a distance s, then continues at constant speed for some time t and then decelerates at the rate f/2 to come to rest. If the total distance is 5 s, then prove that s = ½ ft The position coordinate of a moving particle is given by x = t + 9t 2 (x in metres and t in seconds). What is its velocity at t = 2 sec? 19. Derive kinematic equations of motion for uniformly accelerated motion by Calculus method. 20. Derive kinematic equations of motion for uniformly accelerated motion by Graphical method.

3 CHEMISTRY 1. Calculate the mass of an atom of silver. (Atomic mass of silver = 108 u) 2. Calculate the mass of (i) 1 atom of C 14 (ii) 1 molecule of N 2 (iii) 1 molecule of water (iv) 100 molecules of sucrose (C 12 H 22 O 11 ) 3. Calculate the mass of (i) One atom of calcium. (ii) One molecule of sulphur dioxide (SO 2 ). 4. Calculate the number of atoms in (i) 0.5 mole atoms of carbon (C 12 ) (ii) 3.2 g of sulphur. (iii) 18.0 g of glucose. (iv) 0.2 mole molecules of oxygen. 5. Calculate the mass of sodium which contains same number of atoms as are present in 15 g of calcium. 6. What volume is occupied at NTP by (i) 1.4 g of nitrogen gas. (ii) x molecules of oxygen. (iii) 0.2 mole of ammonia? 7. How many years it would take to spend Avogardro number of rupees at the rate of 10 lakh rupees per second? 8. Calculate the number of molecules and number of atoms present in 5.60 L of ozone at NTP. 9. A dot. containing carbon has 1 mircogram weight. Calculate number of carbon atoms used to make this dot. 10. Calculate the mass of oxygen in grams present in 0.1 mole of Na 2 CO 3.10H 2 O. 11. Calculate the mass percentage of various elements present in magnesium sulphate MgSO An organic compound containing carbon, hydrogen and oxygen gave the following percentage composition: C = % and H = 5.08%. The vapour density of the compound is 59. Calculate the molecular formula of the compound. 13. The elemental composition of butyric acid was found to be 54.2% C, 9.2% H and rest is oxygen. Determine its empirical formula. 14. Calculate the empirical and molecular formula of the compound having the following percentage composition. Na = 36.5%, H = 0.8%, P = 24.6%, O = 38.1%. 15. An oxide of nitrogen contains 30.43% of nitrogen. The molecular weight of the compound is equal to 92 u. Calculate the molecular formula of the compound.

4 Holiday Homework INDRAPRASTHA PUBLIC SCHOOL,KATHA Class-XI Subject:- Computer Science 1. Make a file on various method used for protecting your computer system and your information from malicious attacks. 2. Prepare the topic for presentation IPO cycle Primary/Secondary memory Characteristics of computer system Functional unit of a computer system NOTE:- Complete your class work/home work and learn that.

5 Assignment-1 Topic- Trigonometry 1. Geometrically prove that: I. tan (A+B)= tana +tanb 1 tana.tanb. II. cos(a-b)= cosa cosb + sina SinB. III. Tan2A = 2tanA 1 tan 2 A. 2. Find the value of : I. sin18 II. cos54 III. sin72 IV. cos36 3. Prove that: tana. tan(60-a). tan (60+A) =tan3a. 4. Show that sec 8 A 1 sec 4 A 1 = tan 8 A tan 2 A. 5. Prove that: tan A+ 2tan2A + 4tan4A+ 8cot2A=cotA. 6. Prove that sina.sin(60-a). sin(60+a) = 1 4 sin3a. 7. If cos(b-c)+ cos(c -A)+cos(A -B)= -3/2. Prove that: cos A+ cosb+ cosc = sina+ sinb+ sinc=0 8. Prove that : sin (B C) sin (C A ) sin ( A B) + + cosb cosc cosc cosa cosa cosb 9. Prove that :Tan70 = 2 tan50 + tan20. = If tanθ= b, then find the value of a cos2θ+ b sin2θ. a Prove that cos36 cos72 cos108 cos144 = If A+B+C= π, prove that cosa+cosb+cosc-1= 4sin A/2 sinb/2 sinc/ If A+B+C =180. Prove that sin 2 A/2+ sin 2 B/2+sin 2 C/2= 1-2sinA/2 2sinB/2 sinc/ Find the general value of Θ. 7cos 2 Θ+ 3sin 2 Θ= Solve: tanx + tan2x + tan3x = 0.

ISSUED BY K V - DOWNLOADED FROM KINEMATICS

ISSUED BY K V - DOWNLOADED FROM KINEMATICS KINEMATICS *rest and Motion are relative terms, nobody can exist in a state of absolute rest or of absolute motion. *One dimensional motion:- The motion of an object is said to be one dimensional motion