Question 1 :
A rigid body is said to be in partial equilibrium, when it is in

Question 2 :
A sphere of mass <em>m</em> and radius <em>R</em> is attached with string of length <em>l</em>. The moment of inertia of sphere about an axis passing through point of suspension <em>O</em> and perpendicular to plane of paper is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2d8bfef6349df00fe4b"/>

Question 3 :
Position of two particles are given by <em>x</em>₁ = 2<em>t</em> and <em>x</em>₂ = 2 + 3<em>t</em>. If the velocity of centre of mass at <em>t</em> = 2<em>s</em> is 2.5 m/s. Then velocity of centre of mass at <em>t</em> = 4 s will be

Question 4 :
Let {tex} \vec { F } {/tex} be the force acting on a particle having position vector {tex} \vec { r } {/tex} and {tex} \vec { T } {/tex} be the torque of this force about the origin. Then

Question 5 :
The moment of inertia of a circular wire of mass {tex} m {/tex} and radius {tex} R {/tex} about its diameter is

Question 6 :
Consider a uniform square plate of side {tex} a {/tex} and mass {tex} m {/tex}. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is<br>

Question 7 :
A cylinder of height 20m is completely filled with water. The velocity of efflux of water <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75fdce491ec9580069900c' height='24' width='77' > through a small hole on the side wall of the cylinder near its bottom is [2002]

Question 8 :
The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius <em>r</em>. The distance of the line from the centre is

Question 9 :
For particle of a purely rotating body, v = r&omega;, so correct relation will be -

Question 10 :
Moment of inertia of a circular wire of mass {tex} M {/tex} and radius {tex} R {/tex} about its diameter is<br>

Question 11 :
A disc of radius <em>R</em> rolls on a horizontal surface with linear velocity <em>V</em> and angular velocity ω. There is a point <em>P</em> on circumference of disc at angle θ with upward vertical diameter measured anticlockwise see figure, which has a vertical velocity. Here θ is equal to<img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2e6f1a5a149feab9a47"/>

Question 12 :
When an explosive shell travelling in a parabolic path under the effect of gravity explodes in the mid-air, the centre of mass of the fragments will move

Question 13 :
A solid cube is placed on a horizontal surface. The coefficient of friction between them is <font face="Symbol">&micro;</font>, where <font face="Symbol">&micro;</font> < 1/2. A variable horizontal force is applied on the cube’s upper face, perpendicular to one edge and passing through the mid-point of edge, as shown in figure. The maximum acceleration with which it can move without toppling is<img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2fa1da6d070c2abf9b4"/>

Question 14 :
A spring wrapped on a wheel of MOI 0.2 kg m² and radius 10 cm over a light pulley to support a block of mass 2 kg as shown in fig. Find the acceleration of the block. <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75fc1cb5f89758f2d4fedb' height='126' width='196' >

Question 15 :
A {tex} ' T ' {/tex} shaped object with dimensions shown in the figure, is lying on a smooth floor. A force '{tex} \vec { F } {/tex}' is applied at the point {tex} P {/tex} parallel to {tex} A B , {/tex} such that the object has only the translational motion without rotation. Find the location of {tex} P {/tex} with respect to {tex} C {/tex} <br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dc40b8d4548337453d21337">