Motion In a Plane MHT-CET pyq's

MHT-CET 2005

1. Angular velocity of hour hand of a watch is

• (A) π/43200 rad s^-1 
• (B) π/30 rad s^-1
• (C) π/21600 rad s^1
• (D) π/1800 rad s^-1

MHT-CET 2006   

2. An electric fan has blades of length of 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 rpm. the acceleration of a point on the tip of the blade is about.

• (A) 1600ms^-2
• (B) 4750ms^-2
• (C) 2370ms^-2
• (D) 5055ms^-2

MHT-CET 2011 

3. A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a hotizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which ball can be moved?

• (A) 14 ms^-1
• (B) 3 ms^-1
• (C) 3.92 ms^-1
• (D) 5 ms^-1

MHT-CET 2014 

4. The difference between angular speed of minute hand and second hand of a clock is

• (A) 59π/900 rad/s
• (B) 59π/1800 rad/s
• (C) 59π/2400 rad/s
• (D) 59π/3600 rad/s

MHT-CET 2016

5. Angular speed of hour hand of a clock in degree per second is

• (A) 1/30
• (B) 1/60
• (C) 1/120
• (D) 1/720

MHT-CET 2019

6. A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in m/s² is 

• (A) 2π²
• (B) 4π²
• (C) 8π²
• (D) π²

7. In U.C.M. when time interval δt → 0, the angle between change velocity (δV)and linear velocity (V) will be 

• (A) 0° 
• (B) 45°
• (C) 90° 
• (D) 180° 

8. If the radius of the circular path and frequency of revolution of a particle of mass 'm' are doubled then the change in its kinetic energy will be (Ei and Ef are the initial and final kinetic energies of the particle respectively) 

• (A) 8E_i
• (B) 15E_i
• (C) 12E_i 
• (D) 16 E_i

9. A body of mass 'm' is performing a U.C.M. in a circle of radius 'r' with speed 'v'. The work done by the centripetal force in moving it through (2/3)rd of the circular path is

• (A) mv²πr
• (B) 2πmv^2r/3
• (C) zero
• (D) 2mv²π/3

10. The ratio of the angular speed of the hour hand of a clock to that of its minute hand is 

• (A) 3600 : 1 
• (B) 1 : 24 
• (C) 1 : 12 
• (D) 12 : 1

11. A wheel completes 2000 revolutions to cover the distance of 9.42 km. The diameter of this wheel is π = 3.14 

• (A) 1 cm
• (B) 1 m
• (C) 1.5 cm
• (D) 1.5 m 

12. A particle is performing a uniform circular motion along the circumference of a circle of radius 'R' and 'T' is the periodic time. In the time 'T/4' its displacement and distance covered are respectively

• (A) √2R,  πR/4
• (B) πR/2, √2R
• (C) √2R, πR
• (D) √2R, πR/2
  

13. Two stones of masses m and 3m are whirled in horizontal circles, the heavier one in radius (r/3) and lighter one in radius 'r'. The tangential speed of lighter stone is 'n' times that of the value of heavier stone, when they experience same centripetal force. The value of n is 

• (A) 4
• (B) 1
• (C) 2
• (D) 3

MHT-CET 2020 

14. A vehicle moving with 15 km/hr comes to rest by covering 5m distance by applying brakes. If the same vehicle moves at 45 km/hr, then by applying brakes, it will come to rest by covering a distance 

• (A) 60 m 
• (B)15 m 
• (C) 45 m 
• (D) 30 m

15. A moving body is covering distances which are proportional to square of the time. Then the acceleration of the body is

• (A) constant but not zero
• (B) increasing
• (C) zero
• (D) decreasing

16. A body is just revolved in a vertical circle of radius 'R'. When the body is at highest point, the string breaks. The horizontal distance covered by the body after the string breaks is

• (A) R
• (B) 4R
• (C) 2R
• (D) 3R

17. A particle is moving along the circular path of radius 'r' with velocity 'v'. The magnitu average acceleration after half revolution is 

• (A) 3v²/πr
• (B) 3v²/2πr
• (C) 2v²/πr
• (D) v²/πr

18. Two particles are performing uniform circular motion about a centre of two concentric circles of radii 'r1', and 'r2', respectively. The two particles and the centre of circles lie on a straight during the motion, then the ratio of their angular velocities will be

• (A) 3 : 1 
• (B) 2 : 1 
• (C) 0.5 : 1
• (D) 1 : 1 

19. A particle is moving in uniform circular motion with speed 'V' and radius 'R'. The angular acceleration of the particle is

• (A) V²/R along tangent to the circle.
• (B) zero
• (C) V²/R along the radius towards the centre of the circle 
• (D) V²/R perpendicular to the plane of the circle.
  

20. A stone of mass 3 kg attached at one end of a 2m long string is whirled in horizontal circle. string makes an angle of 45° with the vertical then the centripetal force acting on the string is (g = 10 m/s², tan45° = 1)

• (A) 20 N
• (B) 30 N
• (C) 10 N
• (D) 40 N 

21. A body of mass 'm' is moving along a circle of radius 'r' with linear speed 'v'. Now, to change the linear speed to V/2 and to move it along the circle of radius '4r', required change in the centripetal force of the body is 

• (A) decrease by 15/16 
• (B) decrease by 5/16
• (C) increase by 9/16
• (D) increase by 11/16
  

22. A string of length 'l' is fixed at one end and carries a mass 'm' at the other end. The mass is revolving along a horizontal circle of radius 'r' making 'θ' as the semi-vertical angle of cone and (1/ π) revolutions per second around the vertical axis through fixed end. The tension in the string is

• (A) 2 ml
• (B) 8 ml
• ( C) 4 ml 
• (D) 16 ml
  

23. At any instant, the magnitude of the centripetal force on a particle of mass 'm' performing circular motion is given by (w = angular velocity and v = linear velocity of the particle)

• (A) mw²/v
• (B) mv²/w
• (C) m²w²/v
• (D) mwv
  

24. Mass of 0.5 kg is attached to a string moving in horizontal circle with angular velocity 10 cycle/min. Keeping the radius constant, tension in the string in made 4 times by increasing angular velocity 'w'. The value 'w' of that mass will be

• (A) 1/4 cycle/s
• (B) 1/2 cycle/s 
• (C) 1/5 cycle/s
• (D) 1/3 cycle/s

25. A particle is performing uniform circular motion. If 'θ', 'w', 'α' and 'a' are its angular displacement, angular velocity, angular acceleration and centripetal acceleration respectively, then which of the following is 'WRONG'? 

• (A) w ⊥ v
• (B) v ⊥ a
• (C) w ⊥ α
• (D) w ⊥ a

26. A ball of mass 'm' is attached to the free end of an inextensible string of length '√l''. Let 'T' be the tension in the string. The ball is moving in horizontal circular path about the vertical axis. The angular velocity of the ball at any particular instant will be

• (A) √(Tm/l)
• (B) √(Tl/m)
• (C) √(T/ml)
• (D) √(ml / T)

27. Two cars of masses 'm1'. and 'm2' are moving in the circles of radii 'r1' and 'r2' respectively. Their angular speed 'w1' and 'w2' are such that they both complete one revolution in the same time 't'. The ratio of linear speed of 'm1' to the linear speed of 'm2' is

• (A) w²₁ : w²₂ 
• (B) T²₁ : T²₂ 
• (C) r₁ : r₂ 
• (D) m₁ : m₂

28. A string of length 'l' fixed at one end carries a mass 'm' at the other end. The string makes 3/π revolutions/second around the vertical axis through the fixed end as shown in figure. The tension 'T' in the string is

• (A) 36 ml 
• (B) 3 ml
• (C) 18 ml
• (D) 9 ml

29. A particle performing U.C.M. of radius π/2m makes 'x' revolutions in time 't'. Its tangential velocity is

• (A) πx/t²
• (B) πx²/t
• (C) π²x/t
• (D) πt/x²

30. A mass 'm' is tied to one end of a spring and whirled in a horizontal circle with constant angular velocity. The elongation in the spring is 1 cm. If the angular speed is doubled, the elongation in the spring is 6 cm. The original length of the spring is 

• (A) 3 cm 
• (B) 12 cm 
• (C) 6 cm 
• (D) 9 cm

31. The angular speed of the minute hand of a clock in degrees per second is 

• (A) 0.1 
• (B) 10 
• (C) 1 
• (D) 0.1