JEE Important Chapter - Mechanics

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Mechanics for JEE

Mechanics is a branch of physics that deals with energy and forces and their effect on bodies. As far as JEE Advanced exam is concerned, this chapter covers a vast amount of topics and is thus a very important chapter. This chapter requires conceptual understanding as well as numerical skills to score good marks in JEE Advanced.

In Mechanics, we learn about one dimensional and two dimensional and practical applications of newton’s laws of motion and force system in mechanics. Concepts related to kinetic energy and potential energy are also discussed in detail along with the work-energy theorem.

Problems related to rotational dynamics and gravitation are also important in Mechanics. Concepts related to the properties of solids and liquids as well as thermodynamics are included in this chapter mechanics.

Now, let us see what is mechanics, mechanics definitions, laws of mechanics, important concepts and formulae related to JEE advanced exams along with a few solved examples.

Important Topics of Mechanics

• Motion along two dimension

• Laws of motion

• Mass Pulley system

• Work done by a constant force and variable force

• Kepler’s Law of planetary motion

• Stress-strain curve

• Rotational motion

• Bernoulli’s theorem

• Laws of thermodynamics

Solved Examples

1. A bomb of mass30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velcoity of 18 kg mass is 6 m/s. The kinetic energy of the other mass is ________.

Sol:

The total momentum of the bomb before and after exploision is constant.

$0=m_1v_1+m_2v_2$

$0=18\times 6+12\times v_2$

$v_2=-9~ m/s$

The kinetic energy of the mass having 12 kg is given by,

$K=\dfrac{1}{2}mv^2$

$K=\dfrac{1}{2}\times 12\times 9^2$

$K=486~J$

Therefore, kinetic energy of the other mass is 486 J

Key Point: The total momentum is conserved in the case of explosion of a bomb.

2. The instantaneous angular position of a point on a rotating wheel is given by the equation, $\theta(t)=2t^3-6t^2$ . The torque on the wheel becomes zero at ______.

Sol:

We can find the equation of angular velocity from the angular position as given below,

$\omega=\dfrac{d\theta}{dt}$

$\omega=\dfrac{d}{dt}(2t^3-6t^2)$

$\omega=6t^2-12t$

The equation for angular acceleration of the point is obtained by,

$\alpha=\dfrac{d\omega}{dt}$

$\alpha=\dfrac{d}{dt}(6t^2-12t)$

$\alpha=12t-12$

The torque becomes zero when angular acceleration becomes zero

$\alpha=12t-12$

$0=12t-12$

$t=1~s$

Therefore, torque becomes zero at t =1 s.

Key Point: Differentiating angular velocity with respect to time gives angular acceleration.

Previous Year Questions from JEE Advanced Paper

1. A wire which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on the ground as shown in the figure. The ball is released from near  the top of the wire and it slides along the wire without any friction. As the bead moves from A to B, the force it applies on the wire is  (JEE Advanced 2010)

2. Always radially inwards

3. Radially outwards initially and radially inwards later.

4. Radially inwards initially and radially outwards later.

Sol:

Applying newton’s second law of motion equation,

$mg\cos\theta-\dfrac{mv^2}{R}=N$...(1)

Applying conservation of energy,

$\dfrac{1}{2}mv^2=mgR(1-\cos\theta)$...(2)

Using equation (1) and (2),

$N=mg(3\cos\theta-2)$

So, N is positive when

$0\lt \theta\lt \cos^{-1}\left(\dfrac{2}3{}\right)$

N is negative when

$\theta\gt \cos^{-1}\left(\dfrac{2}3{}\right)$

Therefore, force exerted  on the wire by the bead is radially inwards initially and radially outwards later. So, correct answer is option (D)

Key Point: For a body to move in a circular path, there must be a centripetal force acting on it.

2. Two identical uniform discs roll without slipping on two different surfaces,  AB and CD starting at A and C with linear speeds v1 and v2 respectively, and always remain in contact with surfaces. If they reach B and D with same linear speed v1= 3 m/s and v2= ______.(JEE Advanced 2015)

Sol:

Both discs reach B and D with same speed. Hence, final kinetic energy is same for both disc.

Applying conservation of energy,

For first disc,

$\dfrac{1}{2}I\omega_1^2+mg\times30=K$...(1)

For second disc,

$\dfrac{1}{2}I\omega_2^2+mg\times27=K$.....(2)

Solving equation (1) and equation (2), we get,

$\dfrac{1}{2}\times\left(\dfrac{3}{2}mR^2\right)\times\left(\dfrac{3}{R}\right)^2+mg\times30=\dfrac{1}{2}\times\left(\dfrac{3}{2}mR^2\right)\times\left(\dfrac{v_2}{R}\right)^2+mg\times27$

$v_2=7~m/s$

Key Point: The total mechanical energy is constant if the work is done only by the conservative force.

Practice Questions

1. A constant torque of 1000 Nm turns a wheel of moment of inertia 200 kgm2 about an axis through its centre. Its angular velocity after 3 seconds is  (Ans: 15 rad/s)

2. For a satellite moving in an orbit around the earth, the ratio of kinetic energy to the potential energy is (Ans: 1:2)

Conclusion

In this article we have provided important information regarding the chapter mechanics such as important concepts, formulae, etc.. Students should work on more solved examples along with  previous year question papers for scoring good grades in the JEE advanced exams.

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FAQs on JEE Important Chapter - Mechanics

FAQ

1. What is the weightage of mechanics in JEE Advanced?

Nearly 25% questions are asked in the JEE Advanced exam from this chapter. Mechanics is one of the most important topics and fundamental topic in JEE Advanced.

2. What is the difficulty level of Mechanics in JEE Advanced exam?

Theory of Mechanics is a vast topic and one of the fundamentals of physics required for JEE advanced. The mixed concepts from different types of mechanics topics  can also asked by relating to other topics of JEE Asvanced. Students who are good in mechanics can score good marks in JEE advanced.  Overall, mechanics is a moderate difficult which becomes easier with proper practise and effort. It is better if yo keep mechanics of structure pdf readily available for reference.

3. Are previous year's questions Important for JEE Advanced?

Yes, previous year's JEE Advanced questions are important. Once the student is finished learning concepts and solving problems, they must go through the previous year's question papers the last 20 years to understand the test pattern and frequent questions asked in the exam.