# Mechanics - The ultimate problems for CBSE/NCERT/ IIT -JEE (Main+Advanced) and NEET

## Mechanics

## Part (A) Core

## - Kinematics

## A. Vectors

## B. Straight Line Motion

## C. Motion in Plane (Projectile & Circular Motion)

## - Newton's Laws of Motion (NLM)

## - Friction

## - Work Energy Power

## - Centre of Mass (C.O.M.) & Collisions

## - Rotational Mechanics (Dynamics of Rotational Motion)

## (Part -B) Applied

## -Gravitation

## - Mechanical properties of solids

## - Fluid Mechanics

## - S.H.M. (Simple Harmonic Motion)/Oscillation

## - Waves (Wave Mechanics)

## Q1.A solid disc is rolling without slipping on a horizontal ground as shown in figure. Its total kinetic energy is 150 J . Its translational and rotational kinetic energies respectively are

50 J , 100 J

100 J , 50J

`75 J, 75J `

`125J , 25J`

## Q3.What is the maximum compression in the spring, if the lower block is shifted to rightward with acceleration a. (Given that all surfaces are smooth as shown).

\frac{ma}k

\frac{2ma}k

` \frac{mak}2`

`\frac{ma}{2k}`

## Q4.The density of a rod AB increases linearly from A to B. Its mid-point is O and centre of mass is at C. Four axes pass through A, B, O and C , all perpendicular to the length of rod. The moments of inertia of the rod about these axes are I_{A}, I_{B}, I_{O} and I_{C} respectively. Then

I_{A}> I_{B}

I_{C} < I_{B}

I_{O}> I_{C}

All of these

## Q5. Moment of inertia of a uniform rod of length L and mass M, about an axis passing through L/3 from one end and perpendicular to its length is

\frac2{27}M\;L^2

\frac1{6}M\;L^2

\frac1{12}M\;L^2

\frac19M\;L^2

## Q6.A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest. If the kinetic energy of the balls after collision is \frac34th of the original. Then the coefficient of restitution is

e=\frac1{\sqrt2}

e=\frac12

`e=\frac{\sqrt2}3`

e=\frac13

## Q1.F-x equation of a body of mass 4 kg in S.H.M. is F+\;16x\;=0.Here, F is newton and x in meter. The time period of oscillations will be

6.28\; sec

3.14\; sec

1.57\; sec

1 \; sec

## Q2. A spaceship is launched into a circular orbit close to the earth's surface. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull. Radius of earth =6400 km , g= 9.8 ms^{-2}

3.2 km/s

11.2 km/s

1.5 km/s

## Q3.A geostationary satellite is orbiting the earth at a height of 6R above the surface of earth where R is the radius of earth. The time period of another satellite at a distance of 3.5 R from the centre of earth is

16.96 hours

8.48 hours

9.25 hours

15.76 hours

## Q1.The tension in a string holding a solid block below the surface of a liquid (of density greater than that of solid) as shown in the figure is T_o when the system is at rest. What will be the tension in the string if the system has upward acceleration a.

`T_o\frac ag`

`T_o\left(1-\frac ag\right)`

`T_o\left(1+\frac ag\right)`

`T_o\left(\frac ag-1\right) `

## Q2. A small body of density ρ is dropped from rest at a height h into a lake of density σ , where σ > ρ . What would be of the acceleration of body till it moves inside the lake? (Neglect all dissipative effects)

g\left(\frac\sigma\rho-1\right)\;downwards

g\left(\frac\sigma\rho-1\right)\;upwards

g\left(\frac\sigma\rho\right)\;downwards

g\left(\frac\sigma\rho\right)\;upwards

## Q3.A partially immersed solid block of \rho_s is floating in a liquid of density \rho_L as shown in figure. If beaker container moves up with positive acceleration 'a' , what is correct statement about the block?

It sinks more inside the liquid

It sinks lesser inside the liquid

It neither sinks more nor lesser inside the liquid

Can not be predicted as data is insufficient