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State, for each of the following physica...

State, for each of the following physical quantities, if it is a scalar or a vector. Volume, mass speed acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.

Text Solution

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The correct Answer is:
Volume , mass , speed , density , number of moles , angular frequency are scalars ; the rest are vect
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Knowledge Check

  • If omega_(0), omega are initial and final angular velocities theta is the angular displacement and alpha is the angular acceleration then, choose the correct statement .

    A
    `omrga^(2) = omega_(0)^(2) - 2 alpha theta`
    B
    `omega_(0) ^(2) = omega^(2) - 22 alpha theta`
    C
    `omega_(0)^(2) + omega^(2) + 2 alpha theta`
    D
    `omega^(2) = omega_(0)^(2) + 2 alpha theta`

  • If omega_(0), omega are initial and final angular velocities theta is the angular displacement and alpha is the angular acceleration then, choose the correct statement .

    A
    `omrga^(2) = omega_(0)^(2) - 2 alpha theta`
    B
    `omega_(0) ^(2) = omega^(2) - 22 alpha theta`
    C
    `omega_(0)^(2) + omega^(2) + 2 alpha theta`
    D
    `omega^(2) = omega_(0)^(2) + 2 alpha theta`

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    Classify the following as scalar and vector quantities. (i) Time period (ii) Distance (iii) Force (iv) Velocity (v) Work done

    A uniform rod of mass M and length a lies on a smooth horizontal plane. A particle of mass m moving at a speed v perpendicular to the length of the rod strikes it at a distance a/4 from the centre and stops after the collision. Find a. the velocity of the cente of the rod and b. the angular velocity of the rod abut its centre just after the collision.

    Suppose the particle of the previous problem has a mass m and a speed v before the collision and it sticks to the rod after the collision. The rod has a mass M. a. Find the velocity of the particle with respect to C of the system consituting the rod plus the particle. b. Find the velociyt of the particle with respect to C before the collision. c. Find the velocity of the rod with respect to C before the colision. e. find the moment of inertia of the system about the vertical axis through the centre of mass C after the collision. f. Find the velociyt of the centre of mass C and the angular velocity of the system about the centre of mass after the collision.

    The angular displacement theta radians of a fly wheel varies with time t seconds and follow the equation theta = 9t^(2) - 2t^(3) . Determine the angular velocity and acceleration of the fly wheel when time t =1 seconds and (ii) The time when the angular acceleration is zero.

    A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity omega . If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity:

    The motion of a particle executing simple harmonic motion is described by the displacement function, x(t)=Acos(omegat+phi) . If the initial (t = 0) position of the particle is 1 cm and its initial velocity is omega cm/s, what are its amplitude and initial phase angle ? The angular frequency of the particle is pi s^(-1) . If instead of the cosine function, we choose the sine function to describe the SHM : x = B sin (omegat + alpha) , what are the amplitude and initial phase of the particle with the above initial conditions.

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