Chapter Units and Measurement

Transcription

1 2 Chapter Units and Measurement 1. Identify the pair whose dimensions are equal [2002] torque and work stress and energy force and stress force and work 2. [2003] [L -1 T] ] [L -2 T 2 ] [L 2 T -2 ] [LT -1 ] 3. The physical quantities not having same dimensions are [2003] torque and work momentum and planck s constant stress and young s modulus speed and ( 0 0) -1/2 Ans: 4. Which one of the following represents the correct dimensions of the coefficient of viscosity? [2004] ML -1 T -1 MLT -1 ML -1 T -2 ML -2 T Out of the following pair, which one does NOT have identical dimensions is [2005] impulse and momentum angular momentum and planck s constant work and torque moment of inertia and moment of a force (towards north-west) 6. The dimension of magnetic field in M, L, T and C (coulomb) is given as [2008] MLT 1 C 1 MT 2 C 2 MT 1 C 1 MT 2 C 1 7. A body of mass m = kg is moving along the x-axis with a speed of 5.00 ms 1. The magnitude of its momentum is recorded as [2008] 17.6 kg ms kg ms kg ms kg ms 1 8. Two full turns of the circular scale of a screw gauge cover a distance of 1mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of 0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is [2008] 3.32 mm 3.73 mm 3.67 mm 3.38 mm 9. In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half- a degree (= 0.5 ), then the least count of the instrument is: [2009] half minute one degree half degree one minute 10. The respective number of significant figures for the numbers , and are [2010] 5, 1, 2 5, 1, 5 5, 5, 2 4, 4, A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading: 0 mm Circular scale reading: 52 divisions Given that 1mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is: [2011] cm cm cm 0.52 cm 12. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is: [2012] 6% zero 1% 3%

2 3 13. A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree Vernier scale reading: 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the Vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data: [2012] degree degree degree 59 degree Let [ 0]denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then: [2013] 0 = [M 1 L 3 T 2 A] 0 = [M 1 L 3 T 5 A 2 ] 0 = [M 1 L 2 T 1 A 2 ] 0 = [M 1 L 2 T 1 A] Ans:

3 4 Chapter Motion Kinematics Ans: 1. A ball whose kinetic energy is E, is projected at an angle of 45 to the horizontal. The kinetic energy of the ball at the highest point of its flight will be [2002] E E/ 2 E/2 zero. 2. From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically with the same speed). If va and vb are their respective velocities on reaching the ground, then [2002] vb > va va = vb va > vb their velocities depend on their masses. Ans: 3. A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is [2003] 12 m 18 m 24 m 6 m 4. [2003] 5.20m 4.33m 2.60m 8.66m The co-ordinates of a moving particle at any time t are given by x = αt 3 and y = βt 3. The speed of the particle at time t is given by [2003] 6. A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball at 3/T second [2004] 8h/9 meters from the ground 7h/9 meters from the ground h/9 meters from the ground 17h/18 meters from the ground 7. If A B = B A, then the angle between A and B is [2004] π/2 π/3 π π/4 8. A projectile can have the same range R for two angles of projection. If T1 and T2 to be time of flights in the two cases, then the product of the two time of flights is directly proportional to. [2004] R 1/R 1/R 2 R 2 9. Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed? [2004] The acceleration vector points to the centre of the circle The acceleration vector is tangent to the circle The velocity vector is tangent to the circle The velocity and acceleration vectors are perpendicular to each other. Ans: 10. An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20m. If the car is going twice as fast i.e., 120 km/h, the stopping distance will be [2004] 60 m 40 m 20 m 80 m 11. A ball is thrown from a point with a speed 'v0' at an elevation angle of θ. From the same point and at the same instant, a person starts running with a constant speed v0 /2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection θ? [2004] No Yes, 30 Yes, 60 Yes, 45

4 5 12. 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 f/2 to come to rest. If the total distance traversed is 15 S, then [2005] S = 1/6 ft 2 S = f t S = 1/4 ft 2 S = 1/72 ft A particle is moving eastwards with a velocity of 5 ms -1. In 10 seconds the velocity changes to 5 ms -1 - northwards. The average acceleration in this time is [2005] 17. The velocity of a particle is v = v0 + gt + ft 2. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is [2007] v 0 + g/2 + f v 0 + 2g + 3f v 0 + g/2 + f/3 v 0 + g + f 18. A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x-direction with a constant speed. The position of the first body is given by x1 (t) after time t ; and that of the second body by x2 (t) after the same time interval. Which of the following graphs correctly describes (x1 x2) as a function of time t? [2008] 14. The relation between time t and distance x is t = ax 2 + bx where a and b are constants. The acceleration is [2005] 2bv 3-2abv 2 2av 2-2av A particle located at x = 0 at time t = 0, starts moving along with the positive x-direction with a velocity 'v' that varies as v = α x. The displacement of the particle varies with time as [2006] t 2 t t 1/2 t A particle is projected at 60 o to the horizontal with a kinetic energy K. The kinetic energy at the highest point is [2007] K/2 K Zero K/4 Ans: 19. Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be: [2009]

5 6 13m/s 2 12 m/s m/s 2 14 m/s For a particle in uniform circular motion, the acceleration a at a point P(R, θ) on the circle of radius R is (Here θ is measured from the x-axis) [2010] Ans: [2009] 7 2 units 7 units 8.5 units 10 units 21. [2010] y = x 2 + constant y 2 = x + constant xy = constant y 2 = x 2 + constant 22. [2010] 25. [2010] [2011]

6 7 2 s 4 s 8 s 1 s 30. A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F(t) = F 0 e bt in the x direction. Its speed v(t) is depicted by which of the following curves? 26. A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is: [2011] 27. A particle of mass m is projected with a velocity v making an angle of 30 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height H is [2011] 28. A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be: [2012] 20 2m 10 m 10 2m 20 m 29. Two cars of mass m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is: m1 r1: m2 r2 m1: m2 r1: r2 1: 1 1.

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