CBSE Class 11 Physics Kinematics Worksheet Set B

TOPIC : KINEMATICS

SECTION – A CONCEPTUAL AND APPLICATION TYPE QUESTIONS

Question. A smooth sphere A is moving on a frictionless horizontal plane with angular speed w and centre of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are ωA and ωB, respectively. Then
(a) ωA< ωB
(b) ωA= ωB
(c) ωA= ω
(d) ωB= ω

Answer: C

Question. Two fly wheels A and B are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are 5.0 kg m2 and 20.0 kg m² respectively. Wheel A is made to rotate at 10 revolution per second. Wheel B, initially stationary, is now coupled to A with the help of a clutch. The rotation speed of the wheels will become
(a) 2 5 rps
(b) 0.5 rps
(c) 2 rps
(d) None of these

Answer: C

Question. A wheel is rolling straight on ground without slipping. If the axis of the wheel has speed v, the instantenous velocity of a point P on the rim, defined by angle q, relative to the ground will be 

Answer: B

Question. A uniform bar of mass M and length L is horizontally suspended from the ceiling by two vertical light cables as shown. Cable A is connected 1/4th distance from the left end of the bar. Cable B is attached at the far right end of the bar. What is the tension in cable A?
(a) 1/4 Mg
(b) 1/3 Mg
(c) 2/3 Mg
(d) 3/4 Mg

Answer: C

Question. Acertain bicycle can go up a gentle incline with constant speed when the frictional force of ground pushing the rear wheel is F2 = 4 N. With what force F1 must the chain pull on the sprocket wheel if R₁=5 cm and R₂ = 30 cm?
(a) 4 N
(b) 24 N
(c) 140 N
(d) 35/4 N

Answer: B

Question. Three identical particles each of mass 1 kg are placed touching one another with their centres on a straight line.
Their centres are marked A, B and C respectively. The distance of centre of mass of the system from A is
(a) AB + AC + BC/3
(b) AB + AC/3
(c) AB + BC/3
(d) AC + BC/3

Answer: B

Question. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is
(a) 1 : √2
(b) 1 : 3
(c) 2 : 1
(d) √5 : √6

Answer: D

Question. If the angular velocity of a body rotating about an axis is doubled and its moment of inertia halved, the rotational kinetic energy will change by a factor of :
(a) 4
(b) 2
(c) 1
(d) 1/2

Answer: B

Question. A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60º from the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to keep it from slipping. Choose the correct magnitude from the following.
(a) 175 lb
(b) 100 lb
(c) 120 lb
(d) 17.3 lb

Answer: D

Question. In carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance 1.12 × 10–10 m. The distance of the centre of mass, from the carbon atom is
(a) 0.64 × 10^–10 m
(b) 0.56 × 10^–10 m
(c) 0.51 × 10^–10 m
(d) 0.48 × 10^–10 m

Answer: A

Question. A tube one metre long is filled with liquid of mass 1 kg. The tube is closed at both the ends and is revolved about one end in a horizontal plane at 2 rev/s. The force experienced by the lid at the other end is
(a) 4π²N
(b) 8π²N
(c) 16π²N
(d) 9.8 N

Answer: B

Question. When a bucket containing water is rotated fast in a vertical circle of radius R, the water in the bucket doesn't spill provided
(a) the bucket is whirled with a maximum speed of √2gR
(b) the bucket is whirled around with a minimum speed of √[(1/ 2)gR]
(c) the bucket is having a rpm of √900g /(π²R)
(d) the bucket is having a rpm of √3600g /(π²R)

Answer: C

Question. M.I of a circular loop of radius R about the axis in figure is

(a) MR²
(b) (3/4) MR²
(c) MR²/2
(d) 2MR²

Answer: B

Question. Two rings of radius R and nR made up of same material have the ratio of moment of inertia about an axis passing through centre as 1 : 8. The value of n is
(a) 2
(b) 2√2
(c) 4
(d) 1/2

Answer: A

Question. Four masses are fixed on a massless rod as shown in the adjoining figure. The moment of inertia about the dotted axis is about

(a) 2 kg × m²
(b) 1 kg × m²
(c) 0.5 kg × m²
(d) 0.3 kg × m²

Answer: B

Question. The moment of inertia of a body about a given axis is 1.2 kg m². Initially, the body is at rest . In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad s^–2 must be applied about that axis for a duration of
(a) 4 s
(b) 2 s
(c) 8 s
(d) 10 s

Answer: B

Question. Fig. shows a disc rolling on a horizontal plane with linear velocity v. Its linear velocity is v and angular velocity is w.
Which of the following gives the velocity of the particle P on the rim of the disc 

(a) v (1 + cos θ)
(b) v (1 – cos θ)
(c) v (1 + sin θ)
(d) v (1 – sin θ)

Answer: C

Question. A toy car rolls down the inclined plane as shown in the fig.
It loops at the bottom. What is the relation between H and h? 

(a) H/h = 2
(b) H/h = 3
(c) H/h = 4
(d) H/h = 5

Answer: D

Question. A sphere rolls down on an inclined plane of inclination q.
What is the acceleration as the sphere reaches bottom? 

Answer: A

Question. In a bicycle, the radius of rear wheel is twice the radius of front wheel. If r_F and r_F are the radii, v_r and v_r are the speed of top most points of wheel. Then
(a) v_r = 2v_F
(b) v_F = 2v_r
(c) v_F = v_r
(d) vF > vr

Answer: C

Question. An annular ring with inner and outer radii R₁ and R₂ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring , F₁/F₂ is
(a) (R₁/R₂)²
(b) R₂/R₁
(c) R₁/R₂
(d) 1

Answer: C

Question. A coin placed on a gramophone record rotating at 33 rpm flies off the record, if it is placed at a distance of more than 16 cm from the axis of rotation. If the record is revolving at 66 rpm, the coin will fly off if it is placed at a distance not less than
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

Answer: D

1. Define average and instantaneous velocity.

2. What does the slope of position-time graph indicate?

3. What does the slope of velocity-time graph indicate?

4. Draw the following graphs for an object projected upward with a velocity v0, which comes back to the same point after some time:

(i)Acceleration versus time graph.
(ii)Speed versus time graph.
(iii)Velocity versus time graph

5. Draw position-time graphs for two objects having zero relative velocity.

6. Define: (i) Equal vectors (ii) Negative vector (iii) Unit vector (iv) Null vector.

7. Give two conditions necessary for a given physical quantity to be a vector.

8. State parallelogram law and triangle law of vector addition.

9. Is the rocket in flight an example of projectile?

10. Is it possible to accelerate a particle if it is travelling at constant speed?

 

SECTION – B NUMERICAL PROBLEMS

1. A man walks on a straight road from his home to a market 2.5km away with speed of 5km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5km/h. What is the (a)magnitude of average velocity, and (b) average speed of the man over the interval of time
(i) 0 to 30min , (ii) 0 to 50min , (iii) 0 to 40min?

2. A car moving along a straight highway with speed of 126 km/h is brought to a stop within a distance of 200m.Find the retardation of the car (assumed uniform), and how long does it take for the car to stop?

3. Two balls are thrown simultaneously, ‘A’ vertically upwards with a speed of 20m/s from the ground and ‘B’ vertically downwards from a height of 40m with the same speed and along the same line of motion. At what points do the two balls collide?

4. A body covers 12m in 2^ndsecond and 20m in 4^th second. How much distance will it cover in 4 seconds after the 5^th second?

5. Two trains ‘A’ and ‘B’ of length 400m each are moving on two parallel tracks with a uniform speed of 72 km/h in the same direction, with ‘A’ ahead of ‘B’. The driver of ‘B’ decides to overtake ‘A’ and accelerates by 1 ms-2. If after 50 seconds, the guard of ‘B’ just brushes past the driver of ‘A’, what was the original distance between them?

6. On a two- lane road, car ‘A’ is travelling with a speed of 36km/h. Two cars ‘B’ and ‘C’ approach car ‘A’ in opposite directions with a speed of 54km/h each. At a certain instant, when the distance AB is equal to AC, both being 1km, ‘B’ decides to overtake ‘A’ before C does. What minimum acceleration of car B is required to avoid an accident?

7. Rain is falling vertically with a speed of 30m/s. A woman rides a bicycle with a speed of 10m/s in the north to south direction. What is the relative velocity of rain with respect to the woman? What is the direction in which she should hold her umbrella to protect herself from the rain?

8. In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?

9. An aeroplane take off at an angle of 30⁰ to the horizontal. If component of its velocity along the horizontal is 250km/h, what is the actual velocity of plane? Find also the vertical component of the velocity.

10. A projectile is fired horizontally with a velocity of 98m/s from the top of a hill 490m high. Find (i) the
time taken to reach the ground (ii) the distance of the target from the hill and (iii) the velocity with
which the projectile hits the ground.

11. An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h.
Compare its centripetal acceleration with the acceleration due to gravity.

12. A body is projected with a velocity of 30m/s at an angle of 30⁰ with the vertical. Find the maximum height, time of flight and the horizontal range.

13. Prove that the maximum horizontal range is four times the maximum height attained by a projectile which is fired along the required oblique direction.

14. An insect trapped in a circular groove of radius 12cm moves along the groove steadily and completes 7 revolutions in 100 s .(i) What is the angular speed and the linear speed of the motion? (ii) Is the acceleration vector a constant vector? What is its magnitude?

15. The velocity- time graph of a particle moving along a fixed direction is shown in figure. Obtain the distance travelled by the particle between (i) t = 0 to 10 s (ii) t = 2 to 6 s. What is the average speed of the particle in intervals in (i) and (ii)

16. Two straight lines drawn on the same displacement-time graph make angles 30 ⁰ and 60 ⁰ with time axis respectively, as shown in figure. Which line represents greater velocity? What is the ratio of the two velocities?

17. Acceleration –time graph of a moving object is shown in figure. Draw the velocity-time graph and displacement-time graph corresponding to this type of motion.

18. The velocity-time graph for a vehicle is shown in figure. Draw acceleration-time graph from it.

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