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DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics PDF Download

Introductory Exercise 5.5

Ques 1: In figure m1 = 1 kg and m2 = 4 kg. Find the mass M o f the hanging block which will prevent the smaller block from slipping over the triangular block. All the surfaces are friction less and the strings and the pulleys are light
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
Note In exercises 2 to 4 the situations described take place in a box car which has initial velocity v = 0 but acceleration
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
Ans: 6 .83 kg
Sol: Block on triangular block will not slip if
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
m1a cos θ= m1g sin θ
i.e., a = g tanθ …(i)
N = m1g cosθ + m1asinθ …(ii)
For the movement of triangular block
T - N sinθ = m2α …(iii)
For the movement of the block of mass M
Mg - T = Ma …(iv)
Adding Eqs. (iii) and (iv),
Mg - N sinθ = ( m2 + M )α
Substituting the value of N from Eq. (ii) in the above equation
Mg - (m1g cosθ + m1α sinθ) sinθ
=( m2α + Mα)
i.e., M (g - α) = m1g cosθ sinθ + (m2 + m1 sin2θ)α
Substituting value of a from Eq. (i) in the above equation,
M(1 - tanθ) = m1 cosθ sinθ + ( m2 + m1 sin2 θ) tanθ
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
Substituting θ = 30° , m1 = 1 kg and m2 = 4 kg
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
= 6.82 kg

Ques 2: A 2 kg object is slid along the friction less floor with initial velocity (10 m/s)î (a) Describe the motion of the object relative to car (b) when does the object reach its original position relative to the box car.
Ans:
(a) x = x0 + 10t - 2.5t2 , v = 10 - 5t (b) t = 4s
Sol: (a) Using DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
Displacement of block at time t relative to car would be
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
Velocity of block at time t (relative to car) will be
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
(b) Time (t) for the block to arrive at the original position (i.e., x = x0) relative to car
x0 = x+ 10 t - 2.5 t2
⇒ t = 4s

Ques 3: A 2 kg object is slid along the friction less floor with initial transverse velocity (10 m/s)DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics. Describe the motion (a) in car’s frame (b) in ground frame.
Ans: 
(a) x = x0 - 2.5t2, z = z0 + 10t, vx = - 5t, vz = 10 ms-1 
(b) x = x0, z = z0 + 10t, vx = 0, vz = 10 ms-1
Sol: (a) In car’s frame position of object at time t would be given by      
In car’s frame
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
x = x0 + 0*t + 1/2(-5)t2
i.e., x = x0 - 2.5 t2 …(i)
and z = z + 10t …(ii)
Velocity of the object at time t would be
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
and
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
(b) In ground frame the position of the object at time t would be given by
In ground frame
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
x = x0
and z = z0 + 10t
Velocity of the object at time t would be
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
ans
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics

Ques 4: A 2 kg object is slid along a rough floor (coefficient of sliding friction = 0.3) with initial velocity (10 m/s)î. Describe the motion of the object relative to car assuming that the coefficient of static friction is greater than 0.5.
Ans: 
x = x0 + 10f - 4t2 , K = 10 - 8 t for 0<f<1.25 s object stops at t = 1.25 s and remains at rest relative to car.
Sol: m = 2 kg
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
Normal force on object = mg
Maximum sliding friction = μsmg
= 0.3*2*10 = 6 N
Deceleration due to friction = 6/2 =3 m/s2
Deceleration due to pseudo force  = 5 m/s2
∴ Net deceleration = (3 + 5) m/s2
= 8 m/s2
∴ Displacement of object at any time t (relative to car)
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
Thus, velocity of object at any time t (relative to car)
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
The object will stop moving relative to car when
10 - 8t = 0 i.e., t = 1.25s
∴ vx = 10 - 8t for  0<t<1.25 s

Ques 5: A block is placed on an inclined plane as shown in figure. What must be the frictional force between block and incline if the block is not to slide along the incline when the incline is accelerating to the right at DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
Ans: 
9/25 mg
Sol: For block not to slide the frictional force ( f ) would be given by
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
f + ma cosθ = mg sinθ
or
f = mg sinθ - ma cosθ
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics

The document DC Pandey Solutions: Laws of Motion- 3 | DC Pandey Solutions for NEET Physics is a part of the NEET Course DC Pandey Solutions for NEET Physics.
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FAQs on DC Pandey Solutions: Laws of Motion- 3 - DC Pandey Solutions for NEET Physics

1. What are the three laws of motion?
Ans. The three laws of motion, as proposed by Sir Isaac Newton, are as follows: 1. Law of Inertia: An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an external force. 2. Law of Acceleration: The rate of change of momentum of an object is directly proportional to the force applied to it and takes place in the direction in which the force is applied. 3. Law of Action-Reaction: For every action, there is an equal and opposite reaction.
2. How does Newton's first law of motion apply to everyday life?
Ans. Newton's first law of motion, also known as the law of inertia, can be observed in everyday life situations. For example: - When a car suddenly stops, the passengers continue to move forward due to their inertia. - When a ball is kicked, it eventually comes to a stop due to the force of friction. - When a book is pushed off a table, it falls straight down instead of moving horizontally, as there is no horizontal force acting on it.
3. What is the difference between mass and weight?
Ans. Mass and weight are two different concepts in physics: - Mass refers to the amount of matter present in an object, and it remains constant regardless of the location. Mass is measured in kilograms (kg). - Weight, on the other hand, is the force exerted on an object due to gravity. It varies with the location and is measured in newtons (N). Weight can be calculated by multiplying an object's mass by the acceleration due to gravity (9.8 m/s^2 on Earth).
4. How does Newton's second law of motion explain acceleration?
Ans. Newton's second law of motion states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Mathematically, it can be expressed as F = ma, where F is the net force, m is the mass of the object, and a is its acceleration. This law explains that the greater the force applied to an object, the greater its acceleration will be. Similarly, the smaller the mass of an object, the greater its acceleration will be for a given force.
5. Can an object be at rest and still have forces acting on it?
Ans. Yes, an object can be at rest and still have forces acting on it. According to Newton's first law of motion, an object at rest tends to stay at rest unless acted upon by an external force. Therefore, even if an object is not in motion, it can experience various forces acting on it, such as gravitational force, frictional force, or applied forces. These forces may not be sufficient to overcome the object's inertia and put it into motion, but they still exist.
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