1. A ball is thrown straight up. What is its velocity and acceleration at the highest point? 2. Name two quantities with (i) same dimensions (ii) constant value having dimension. 3. Two straight lines A and B drawn on the same displacement time graph make angles 300 and 600 with time axis respectively. Which line represents the greater velocity? What is the ratio of the velocity of the line A to the velocity of line B ? 4. What is the ratio of SI to CGS unit of acceleration ? 5. What is the angle of projection at which the hmax and Range of a projectile are equal ? 6. The electron revolves around the nucleus of the atom. What is the source of centripetal force ? 7. Two masses are in the ratio 1 : 5. What is the ratio of their inertia ? 8. When a bomb thrown obliquely explodes in midair, at its highest point, what is the direction of motion of its core ? 9. What are random errors? Explain with the help of suitable examples. 10 By using the method of dimension, check the accuracy of the following formula T = rhρg/ 2cosθ , where T is the surface tension (force per unit length), h is the height of the liquid in the capillary tube, ρ is the density of the liquid, g is the acceleration due to gravity, θ angle of the contact, r is the radius of the capillary tube. 11 A planet moves round the sun in a circular orbit. The time period of revolution T of the planet depends on. (i) Radius of the orbit (R) (ii) Mass of the sun M (iii) Gravitational constant G. Show dimensionally that T2 α R3 12 If the length and the time period of an oscillating pendulum have errors of 1% and 2% respectively, what is the error in the estimate of g? 13 The position coordination of a moving particle is given by x = 6 + 18t + 9t2 ( x in metres and t in seconds ). What is its velocity and acceleration at t = 2sec? 14 Explain the terms (i) Instantaneous velocity and (ii) Average velocity ? 15 A ball is thrown vertically up with a velocity of 20m/Sec. Construct time acceleration and time displacement graph. 16 A swimmer can swim with a velocity of 10 km/h. with respect to water flowing in a river at 5km/h. In what direction should he swim to reach the point on the other bank just opposite to his starting point ? 17 A and B are two vectors. Find the magnitude of each vector and angle between these vectors. A = 2i + 3j + k ; B = 4i 2j -2k. 18 State the law of conservation of linear momentum and prove it using third law of motion. 19 Sketch a graph to show the variation of velocity with time of a body moving in a straight line with uniform acceleration. Use this graph and derive the relation, v2 = u2 + 2as where the symbols carry usual meaning. 20 A body covers 200 cm in the first 2 seconds and 220cm in the next 2 seconds, What will be its velocity at the end of 7 seconds? Also, find the displacement in 10 seconds. 21 State the law of parallelogram of vectors. Find the magnitude and direction of the of the resultant of two vectors A and B acting in different directions. 22 From the top of a building 19.6 m high, a ball is projected horizontally. After how long does it strike the ground ? If the line joining the point of projection to the point where it hits the ground makes an angle of 450 with the horizontal, what is its initial velocity of the ball. 23 On a certain day rain was falling vertically with a speed of 30 m/Sec. Suddenly the wind starts blowing from north to south with a speed of 10 m/sec. In which direction should a girl waiting at a bus stop turn her umbrella ? Explain with labelled diagram. 24 The driver of a three- wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and bring his vehicle to rest in 4s just in time to save the child. What is the average retarding force on the vehicle ? The mass of the three- wheeler is 400 kg and the mass of the driver is 65 kg. 25 A batsman deflects a ball by an angle of 600 without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball ? The mass of the ball is 0.15 Kg. 26 A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate of f/2 to come to rest. If the total distance traversed is 5S, then prove that S = ½ ft2. 27 What are the characteristics of a standard unit? 28 a. From the top of a tower 100m in height, a ball is dropped, and at the same time another ball is projected vertically upwards from the ground with a velocity of 25 m/s. Find when and where the two balls meet. Take g = 9.8 m/s2. b. A body starts accelerating uniformly from a velocity u and travels in a straight line. Prove that it covers a length of u +(a/2) ( 2t -1 ) in the tth second of motion. OR Derive an equation for the distance covered by a uniformly accelerated body in n seconds of its motion. A body travels half its total path in the last second of its fall from rest. Calculate the time of its fall. 29 a. A projectile is fired with a velocity u making an angle θ with the horizontal. Obtain expressions for maximum height, total time of flight and the horizontal range. b. An aircraft executes a horizontal loop of radius 1.00km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity. OR a. Define projectile. Show that the path of an oblique projectile is a parabola. b. Prove that the maximum horizontal range is four times the maximum height of the projectile when it is projected at an inclination so as to have maximum range. 30 a. What is parallax method? How do we use this method to estimate the distance of a nearby star? b. If ( P + a/V2) (V-b) = RT, where P=pressure, V= volume, R= Gas constant and T=temperature, then write the dimensions of a/b. OR a. A sign board on the road displays The road is controlled by RADAR. State the principle and explain its function. Suggest two more examples based on this principle.
b. Write dimensions of a/b in the relation F= a√(x) + bt2 where F is force , x = distance and t is time.
1) When a ball is thrown upward, velocity at the highest point is zero and acceleration is due gravity 9.8 m/s2 in downward direction.
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