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**Q.1. Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is : [2020]A: g/5B: g/10C: gD: g/2**

**Q 2. A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : (g 10 m/s ^{2}) [2019]**

B: 10/2π rad/s

C: 10 rad/s

D: 10π rad/s

Ans:

For equilibrium of the block limiting friction

f_{L}≥ mg

⇒ μN ≥ mg

**Q 3. A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when: [2019]A: The mass is at the highest pointB: The wire is horizontalC: The mass is at the lowest pointD: Inclined at an angle of 60° from verticalAns: **C:

The tension is maximum at the lowest position of mass, so the chance of breaking is

maximum.

Then x

A: 1: √2

B: √2: 1

C: 1: √3

D: 1: 2√3

Ans:

A: Rolling friction is smaller than sliding friction

B: Limiting value of static friction is directly proportional to normal reactions

C: Frictional force opposes the relative motion

D: Coefficient of sliding friction has dimensions of length [2018]

Ans:

A:

B:

C: a = g cos θ

D: a = g tan θ

Ans:

**Q 7. Two blocks A and B of masses 3 m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively :- [2017]****A: B: g, gC: D: Ans:** A

A: √5gR

B: √gR

C: √2gR

D: √3gR

Ans:

The question is illustrated in the figure below,

Let, the tension at point A be TA.

Using Newton's second law, we have

Energy at point C is,

At point C, using Newton's second law,

In order to complete a loop, T_{c }≥ 0

so,

From equation (i) and (ii)

Using the principle of conservation of energy,**Q 9. A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 x 10 ^{-4}J by the end of the second revolution after the beginning of the motion ? [2016]A: 0.2 m/s^{2}**

Given, mass of particle. m = 0.01 kg

Radius of circle along which particle is moving , r = 6.4 cm

Kinetic energy of particle, K.E. = 8 x 10^{-4} J

Given that, KE of particle is equal to 8 x 10^{-4} J by the end of second revolution after the beginning of the motion of particle.

It means, initial velocity (u) is 0 m/s at this moment.

Now, using the Newton's 3rd equation of motion,**Q 10. A car is negotiating a curved road of radius R. The road is banked at an angle .. The coefficient of friction between the tyres of the care and the road is 1s. The maximum safe velocity on this road is: [2016]A: B: C: D: Ans:** C

The given situation is illustrated as:

In the case of vertical equilibrium,

Dividing Eqns. (i) and (ii), we get

**Q 11. Three blocks A, B and C, of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is : [2015]**

**A: 18 NB: 2 NC: 6 ND: 8 NAns:** C

a =14/7 = 2m/s

∴ 14 - N

N

A: W(D-x)/d

B: Wx/d

C: Wd/x

D: W(d-x)/x

Ans:

**Q 13. A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is : [2015]A: B: C: D: Ans:** C

**Q 13. A block A of mass m _{1} rests on a horizontal table. A lights string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m_{2} is suspended. The coefficient of kinetic friction between the block and the table is μ_{k}. When the block A is sliding on the table, the tension in the string is: [2015]** D

A:

B:

C:

D:

Ans:

See figure alongside

Let T be the tension in the string.

Let a be the acceleration of the combination

From Equation (2) and (3) we get,**Q 15. A balloon with mass ‘m’ is descending down with an acceleration ‘a’(where a<g). How much mass should be removed from it so that it starts moving up with an acceleration ‘a’ ? [2014]A: B: C:D: **

Let the up thrust on balloon be U.

mq - U = ma ...(i)

If Δm is removed

U = (m - Δm)g = (m - Δm)a ..(ii)

**Q 16. A system consists of three masses m _{1}, m_{2} and m_{3} connected by a string passing over a pulley P. The mass m_{1} hangs freely and m_{2} and m_{3} are on a rough horizontal table (the coefficient of friction = μ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m_{1} is :**

(Assume m_{1} = m_{2} = m_{3} = m) [2014]

B:

C:

D:

Ans:

**Q 17. The force F acting on a particle of mass m is indicated by the force-time graph as shown below. The climate change in momentum of the particle over the time interval from zero to 8s is, [2014]**

**A: 12 NsB: 6 NsC: 24 NsD: 20 NsAns:** A

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