Recent questions in System of Particles and Rotational Motion

The moment of inertia of a uniform rectangular plate about an axis passing through its midpoint and parallel to its length l is

asked Nov 25, 2013 by meena.p

1 answer

If the moment of inertia of a disc about an axis tangential and parallel to the surface is I.Then find the moment of inertia about the axis tangential but perpendicular to the surface in terms of the I?

asked Nov 25, 2013 by meena.p

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Three rings each of mass M and radius R are arranged as shown. The moment of inertia of the system about $YY'$ will be

asked Nov 25, 2013 by meena.p

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The moment of inertia of a sphere of mass M and radius R about an axis passing through centre is $\large\frac{2}{5}\;$$MR^2$. The radius of gyration of the sphere about a parallel axis to the sphere is

asked Nov 25, 2013 by meena.p

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On a uniform rod of length l and mass M, two identical masses m are kept at the extreme ends. What is the moment of inertia of the system about an axis passing through its center and perpendicular to its length ?

asked Nov 25, 2013 by meena.p

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A torque of $20\; Nm$ acting on a rigid body produces are angular acceleration of $4 rad /s^2$ What is the moment of inertia of the rigid body rotating about the fixed axis?

asked Nov 25, 2013 by meena.p

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A torque of $30\; N-m$ is applied on a 5 kg wheel whose moment of inertia is $2 kg\;m^2$ for $10 \;seconds$. The angle covered by the wheel in $10\; s$ will be

asked Nov 25, 2013 by meena.p

1 answer

A wheel has moment of inertia $5 \times 10^{-3} kg m^2$ and is making $20\; kw/s$ The torque needed to stop it in 10 s is

asked Nov 25, 2013 by meena.p

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A particle of mass m is projected with a speed U at an angle $\theta$ with the horizontal. Find the torque of the weight of the particle about the point of projection when the particle is at the highest point .

asked Nov 25, 2013 by meena.p

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A force $\overrightarrow {F} = 3 \hat i +2 \hat j -4 \hat k$ acts at the point $(1,-1,2)$. Whta is its torque about the point $(2,-1,3)$?

asked Nov 25, 2013 by meena.p

1 answer

A simple pendulum of length l is pulled aside to make an angle $\theta$ with the vertical. What is the magnitude of the torque of the weight of the bob about the point of suspension ?

asked Nov 25, 2013 by meena.p

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What is the torque of the force $\overrightarrow {F}=-3 \hat i +\hat j+ 5 \hat k$ acting at a point whose position vector vector is $\overrightarrow {r}= 7 \hat i+3 \hat j +\hat k?$

asked Nov 25, 2013 by meena.p

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Two particles A and B each of mass m are attached by a light inextensible string of length 2l. The whole system lies on a smooth horizontal table with B initially at a distance l from A. The particle at the end B is projected across the table with speed is perpendicular to AB. velocity of ball A just after the **** is

asked Nov 24, 2013 by meena.p

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A particle of mass m and velocity V collides obliquely elastically with a stationary particle of mass 'm'. The angle between the velocity vectors of the two particles after the collision is

asked Nov 24, 2013 by meena.p

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A particle of mass m strikes elastically with a disc of radius R, with a velocity $\overrightarrow {v}$ as shown. If the mass of the disc is equal to that of the particle and the surface of contact is smooth, then the velocity of disc just after the collision is

asked Nov 24, 2013 by meena.p

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A sphere of mass $m_1= 2 kg$ collides with a sphere of mass $m_2= 3 kg$ which is at rest. Mass $m_1$will move at right angles to the line joining the centres at the time of collision,the coefficient of restitution is

asked Nov 24, 2013 by meena.p

1 answer

A small ball on a friction less horizontal surface moves towards right with velocity V. It collides with the wall and return back and continues to and fro motion. If the average speed for first to and fro motion of the ball is $\bigg(\large\frac{2}{3} V\bigg)$, then the coefficient of restitution of impact is

asked Nov 24, 2013 by meena.p

1 answer

Two particles approach each other with different velocities. After collision , one of the particles has a momentum $\overrightarrow {p}$ in their center of mass frame. In the same frame, the momentum of the other particle is

asked Nov 24, 2013 by meena.p

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A particle falls from a height 'h' upon a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled before it stops rebounding is

asked Nov 23, 2013 by meena.p

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In an elastic collision between two bodies, during the time collision is taking place, which physical quantity is conserved?

asked Nov 23, 2013 by meena.p

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In an inelastic collision between two bodies, the physical quantity that is conserved

asked Nov 23, 2013 by meena.p

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A body 'A' experiences perfectly elastic collision with a stationary body 'B'. If after collision the bodies fly apart in opposite directions with equal velocities , the mass ratio of 'A' and 'B' is

asked Nov 23, 2013 by meena.p

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Two particles having position vectors $\overrightarrow {r_1}= (3 \hat i - 5 \hat j)m$ and $\overrightarrow {r_1}= (-5 \hat i +3 \hat j)m$ are moving with velocities $\overrightarrow {V_1}= (-4 \hat i +3 \hat j)m/s$ and $\overrightarrow {V_2}= (-a \hat i +7 \hat j)m/s$. If the collide after 2 seconds, the value of a is

asked Nov 23, 2013 by meena.p

1 answer

A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off at right angles to each other , one with velocity $2 \hat i \;m/s$ and the other with velocity $3 \hat j\; m/s$. If the explosion takes place in $10^{-5}s,$ the average force acting on the third piece in Newtons is

asked Nov 23, 2013 by meena.p

1 answer

A body 'X' with momentum 'p' collides with another identical stationary body ' y ' one dimensionally. During collision ' y' gives an impulse ' J ' to the body 'x'. Then the coefficient of restitution is

asked Nov 22, 2013 by meena.p

1 answer

In two separate collisions the coefficient the coefficient of restitution s $e_1$ and $e_2$ are in the ratio $3:1$ . In the first collision, the relative velocity of approach is twice the relative velocity of separation, then the ratio between the relative velocity of approach and relative velocity of separation in the second collision is

asked Nov 22, 2013 by meena.p

1 answer

A sphere of mass m moving with constant velocity $V$ collide head on with another stationary sphere of same mass. If e is the coefficient of restitution then the ratio of the final velocities of the first and second sphere is

asked Nov 22, 2013 by meena.p

1 answer

A sphere of mass m moving horizontally $V_0$ collides against a pendulum bob of mass m. If the two masses stick together after the collision then the maximum height attained is

asked Nov 22, 2013 by meena.p

1 answer

A bomb is projected vertically up with a velocity of $100 m/s.$ After $8\; s$ it blasted into two pieces of mass in the ratio $1:2$ . The lighter piece goes it with the velocity $40 \;m/s$ then what is the velocity of the heavier piece just after blasting?

asked Nov 22, 2013 by meena.p

1 answer

A body of mass m moving with a constant velocity V hits another body of the same mass moving with velocity V but in the opposite direction and sticks to it. The velocity of the compound body after collision is

asked Nov 22, 2013 by meena.p

1 answer

A rope thrown over a pulley has a ladder with a man of mass m on one of its ends and a counter balancing mass M on its other end. The man climbs with velocity $V_r$ relative to the ladder. Ignoring the masses of the pulley as well as the friction on the pulley axis, the velocity of the centre of mass of this system is

asked Nov 22, 2013 by meena.p

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A system of two blocks A and B and a wedge C are released from rest as shown in figure. Masses of the blocks and the wedge are $m,2m \;and \;2m$ respectively. The displacement of the wedge C when the block slides down the plane a distance 10 cm is (neglect friction)

asked Nov 22, 2013 by meena.p

1 answer

Two particles of equal mass are projected from the ground with speed $v_1$ and $v_2$ at angles $\theta_1$ and $\theta_2$ as shown. The center of mass of the two particles

asked Nov 22, 2013 by meena.p

1 answer

Mass is non- uniformly distributed on the circumference of a ring of radius a and centre at the origin. Let b be the distance of the centre of mass from the origin. Then

asked Nov 22, 2013 by meena.p

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A man of mass $80\; kg$ is riding on a small cart of mass $40\; kg$ moving with velocity $2m/s$ . He is running on the cart, so that his velocity relative to the cart is $3 m/s$ in the direction opposite to the motion of the cart. What is the speed of center of mass of the system.

asked Nov 22, 2013 by meena.p

1 answer

Two blocks of masses $m_1=2 kg$ and $ m_2=4kg$ are moving in the same direction with speeds $V_1=6 m/s$ and $V_2=3 m/s$, respectively on a frictional less surface. An ideal spring with spring constant $k= 30000\;n/m$ is attached to the bakside of $m_2.$ Then the maxiimum compression of the spring after collision will be

asked Nov 22, 2013 by meena.p

1 answer

Tow blocks $m_1$ and $m_2$ are placed on a smooth horizontal surface and are joined together with a spring of stiffness k. Suddenly, block $m_2$ receives a horizontal velocity $v_0$, then the maximum extension $x$ in the spring is

asked Nov 22, 2013 by meena.p

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The momentum of a moving particle is vectorially given as $\overrightarrow{p}=p_0(\cos t \hat {i}+\sin t \hat {j}).$ Where t stands for time.

asked Nov 22, 2013 by meena.p

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Two blocks of masses $6\; kg$ and $4\;kg$ are attached to the two ends of a massless string passing over a smooth fixed pulley. If the system is released, the acceleration of the centre of mass of the system will be ;

asked Nov 22, 2013 by meena.p

1 answer

A particle of mass $200\;g$ is dropped from a height of $50\;m$ and another particle of mass $100\; g$ is simultaneously projected up from the ground along the same line with a speed of $100\; m/s$. The acceleration of the centre of mass after $1\; s$ is

asked Nov 22, 2013 by meena.p

1 answer

A cracker is thrown into air with a velocity of $10 m/s$ at an angle of $45^{\circ}$ with the vertical. When it is at a height of $0.5 \;m$ from the ground it explodes into a number of pieces which follow different parabolic paths. What is the velocity of the centre of mass when it is at a height of $1 \;m$ from the ground. $(g=10\;m/s^2)$

asked Nov 22, 2013 by meena.p

1 answer

A particle of mass 4 m which is at rest explodes into three fragments. Two of the fragments each of mass m are found to move with speed V each in mutually perpendicular directions. The minimum energy released in the process of explosion is

asked Nov 22, 2013 by meena.p

1 answer

Two particles A and B initially at must move towards each other under a mutual force of attraction. The speed of the center of mass at the instant speed of A is V and the speed of B is 2V is

asked Nov 21, 2013 by meena.p

1 answer

Internal forces in a system can change

asked Nov 21, 2013 by meena.p

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Two particles having mass ratio $n:1$ are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of centre of mass of the system is

asked Nov 21, 2013 by meena.p

1 answer

A uniform sphere is placed on a smooth horizontal surface and a horizontal force f is applied on it at a distance h above the center. The acceleration of the center of mass of the sphere

asked Nov 21, 2013 by meena.p

1 answer

Two particles of equal mass have velocities $\overrightarrow{V_1}=4 \hat {i}$ and $V_2= 4 \hat {j} m/s$. First particle has an accleration $\overrightarrow{a_1}=(5 \hat i+5 \hat{j})m/s^2$ While the acceleration of the other particle is zero. The center of mass of the two particles moves in a path of

asked Nov 21, 2013 by meena.p

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A trolley of mass 360 kg lying on a horizontal friction less surface. A man of mass 40 kg runs with uniform speed on the trolley a distance of 2 m in $0.5 \;s$. What is the velocity of the trolley relative to the earth?

asked Nov 21, 2013 by meena.p

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A man of mass 40 kg is standing on a uniform Planck of mass 60 kg lying on a horizontal friction less ice. The man walks from one end to the other end of the Planck. The distance walked by the man relative to ice is (length of Planck=5 m)

asked Nov 21, 2013 by meena.p

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A shell projected from a level ground has a range R, it does not explode. At the highest point the shell explodes into two fragments having masses in the radio 1:3 with each fragment moving horizontally immediately after the explosion. If the lighter fragment falls at a distance R from the point of projection, the distance at which the other fragment falls from the point of projection is

asked Nov 21, 2013 by meena.p

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