Question 1 :
A wheel has moment of inertia 5 x $10^{-3} kg m^2$ and is making 20 rev/sec. The torque needed to stop it in 10 sec is ................ x $10^{-2}N -m$ :-
Question 3 :
A ring of mass mass $m$ and radius $r$ is melted and then molded into a sphere. The moment of inertia of the sphere will be:<br/>
Question 4 :
A thin uniform wire of mass $m$ and length $l$ is bent into a circle. The moment of the inertia of the wire about an axis passing through its one end and perpendicular to the plane of the circle is:
Question 5 :
$I$ is the moment of inertia of a thin circular plate about an axis of rotation perpendicular to the plane of plate and passing through its centre. The moment of inertia of same plate about an axis passing through its diameter is :<br/>
Question 6 :
The advantages of being short and stocky is that you're less likely to get knocked over. This is because
Question 8 :
Consider the following two statements A and B and identify the correct choice.<br/>A) The moment of inertia of a rigid body is independent of its angular velocity.<br/>B) The radius of gyration of a rotating metallic disc is dependent on its temperature.<br/>
Question 9 :
Which of the following order is true for final linear velocity of the bodies
Question 10 :
A sparrow flies around a circular path at a constant speed. If the radius of the circular path is 15.0 m and the sparrow takes 10 seconds to complete one lap. how fast is the sparrow flying?
Question 11 :
A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$ and another plate $Y$ of radius $4R$ is made from an iron late of thickness $\frac { t } { 4 }$ . The ratio between moments of inertia $\frac { I _ { x } } { I _ { x } }$ is
Question 12 :
One can lean further to one side or the other without creating enough turning force to tip him over. This is because
Question 14 :
A motor cyclist takes a U-turn in $4$ seconds. His angular velocity will be _______ $rads^{-1}$.<br/>
Question 15 :
A particle is moving with uniform speed $0.5\ m/s$ along a circle of radius $1\ m$. Then the angular velocity of particle is:<br/>
Question 16 :
The centre of gravity of an object is ______ whether it is placed near the surface of the Earth or near the surface of the Moon.
Question 17 :
From the following, find the pair of physical quantities which are analogous to one another in translatory motion and rotatory motion:<br/>
Question 18 :
The instantaneous velocity of a point on the outer edge of a disk with a diameter of 4 m that is rotating at 120 revolutions per minute is most nearly:
Question 20 :
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping the mass same without applying any external force, which one of the following will not be affected?<br/>
Question 21 :
The angular momentum of an electron in a hydrogen atom is proprotional to ( where r is redius of orbit)
Question 23 :
The length of the second hand of a watch is $2\ cm$, then:<br/>
Question 24 :
A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from $20\pi$ ${rad/sec}$ in $10$ seconds. How many rotation did it make the that period:
Question 25 :
A uniform meter scale of mass $1  kg$ is placed on table such that a part of the scale is beyond the edge. If a body of mass $0.25  kg$ is hung at the end of the scale then the minimum length of scale that should lie on the table so that it does not tilt is :<br/>
Question 26 :
A body of mass 1 kg has a kinetic energy of motion 8 J. Its linear momentum is equal to:
Question 27 :
What is the torque of the force $\vec F=(2\hat i -3\hat j+4\hat k)N$, acting at the point $\vec r=(3\hat i+2\hat j+3\hat k)m$ about the origin (in $N-m$):
Question 28 :
$\mathrm{A}$ particle moves in x-y under the action of the force $\vec{\mathrm{F}}$ Such that $\mathrm{x}$ and $\mathrm{y}$ components of linear momentum, $\vec{\mathrm{P}}$ at any time $\mathrm{t}$ are  $  2\cos \mathrm{t}$ and  $ 2 \sin \mathrm{t}.\ \mathrm{F}$ind the angle between $\vec{\mathrm{F}}\&\vec{\mathrm{P}}$ at a given time<br/>
Question 29 :
A parallelopiped has edges described by the $ \hat i + 2 \hat j$, $4 \hat j$ and $\hat j + 3 \hat k $. Then the volume is:
Question 30 :
A solid cylinder of mass, $m$, and radius, $r$, is rotating at an angular velocity, $\omega$ when a non-rotating hoop of equal mass and radius drops onto the cylinder.<br>In terms of its initial angular velocity, $\omega$, what is its new angular velocity, ${\omega}^{\prime}$?
Question 31 :
The unit vector perpendicular to the plane containing $\vec{A},\vec{B}$ such that $\vec{A}=4\hat{i}-\hat{j}-\hat{k}$ and  $\vec{B}=4\hat{i}+\hat{j}-4\hat{k}$ is:<br/>
Question 32 :
A metal square of mass M has a moment of inertia = I about an axis perpendicular to the plane of the lamina passing through the Centre of gravity. If the mass is reduced to half of its mass and the side of the square is reduced to a/3, what will be the new moment of inertia
Question 33 :
A large, massive man and a small boy of small mass are held far apart on an icy surface where friction is negligible. The man and the boy hold opposite ends of a bungee cord that is stretched.<br>When the boy and the man are released, they are each pulled by the bungee cord so that they approach one another.<br>When they get close to each other, how will their momenta, velocity, and kinetic energies compare?
Question 34 :
Two small spheres of masses 10 kg and 30 kg are joined by a rod of length 0.5 m and of negligible mass. The M.I. of the system about a normal axis through centre of mass of the system is
Question 35 :
A magnetic needle lying parallel to a magnetic field requires $W$ units of work to turn it through $60^{o}.$ The torque required to maintain the needle in this position is
Question 36 :
The moment of inertia of a fly-wheel is $4\, kg\ m^2$. A torque of $10$ Newton-meter is applied on it. The angular acceleration produced will be :
Question 37 :
Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,
Question 38 : <p>A uniform heavy disc of moment of inertia $\displaystyle{I_1}$ is rotating with constant angular velocity $\displaystyle{\omega_1}$. Then, a second nonrotating disc of moment of inertia $\displaystyle{I_2}$ is dropped on it. The two discs rotate together. The final angular velocity of the system becomes</p>
Question 39 :
If $\vec a+\vec b+\vec c=0$ then $\vec a\times \vec b$ is
Question 40 :
If the vectors $\hat {i}+\hat {j}+\hat {k}$ and $3\hat {i}$ form two sides of a triangle, the area of the triangle is........ .
Question 41 :
A hoop of mass $m$ is projected on a floor with linear velocity ${v}_{0}$ and reverse spin ${\omega}_{0}$. The coefficient of friction between the hoop and the ground is $\mu$. How long will it continue to slip after its centre of mass becomes stationary?
Question 42 :
The kinetic energy $T$ of a particle moving along a circle of radius $R$ depends on the distance covered as $T=as^{2}$. The force acting on the particle is:<br/>
Question 43 :
A hoop of mass $m$ is projected on a floor with linear velocity ${v}_{0}$ and reverse spin ${\omega}_{0}$. The coefficient of friction between the hoop and the ground is $\mu$.<br/>Under what condition will the hoop return back?<br/>
Question 44 :
A solid sphere is rolling without slipping on a level surface at a constant speed of $2.0\ ms^{-1}$. How far can it roll up a $30^{o}$ ramp before it stops?
Question 45 :
A and B are two solid spheres of equal masses. A rolls down an inclined plane without slipping from a height $H$. B falls vertically from the same height. Then on reaching the ground.<br/>
Question 46 :
What is the ratio of the linear speeds for the tips of hour and minute hands of a clock if the minute hand is $2.5$ times longer than the hour hand?
Question 47 :
A circular track has a circumference of 3140 m with AB as one of its diameter shooter moves from A to B along the circular path with a uniform speed of 10
Question 48 :
A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping through these motion). The direction of the frictional force acting on cylinder are
Question 49 :
A solid cylinder rolls down an inclined plane. Its mass is $2  kg$ and radius $0.1  \ m$. If the height of the inclined plane is $4  m$, its rotational kinetic energy, when it reaches the foot of the plane is:<br/>
Question 50 :
A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter $1  m$. A mass of $2  kg$ is tied to the end of the cord and it is allowed to fall from rest. The weight falls $2  m$ in $4  s$. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. The angular acceleration produced is:(take $g=10  ms^{-2}$) <br/>
