Laws of Motion

  • Question 489
    CBSEENPH11020323

    A pulley of radius 2m is rotated about its axis by a force F = (20t - 5t2) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg-m2, the number of rotations made by the pulley before its direction of motion if reversed is

    • more than 3 but less than 6

    • more than 6 but less than 9

    • more than 9

    • less than

    Solution

    A.

    more than 3 but less than 6

    To reverse the direction
    integral τdθ space equals 0
straight tau space equals space left parenthesis 20 space straight t minus 5 straight t squared right parenthesis 2 space equals space 40 straight t minus 10 straight t squared
straight alpha space equals space straight tau over straight I space equals space fraction numerator 40 straight t minus 10 straight t squared over denominator 10 end fraction space equals space 4 straight t minus straight t squared
straight omega space equals space integral subscript 0 superscript straight t space αdt space equals space 2 straight t squared minus straight t cubed over 3
straight omega space is space zero space at
2 straight t squared minus straight t cubed over 3 space equals space 0
straight t cubed space equals space 6 straight t squared
straight t space equals space 6 space sec
straight theta space equals space integral ωdt
space equals space integral subscript 0 superscript 6 left parenthesis 2 straight t squared minus straight t cubed over 3 right parenthesis dt
open square brackets fraction numerator 2 straight t cubed over denominator 3 end fraction minus straight t to the power of 4 over 12 close square brackets subscript 0 superscript 6 space equals space 216 space open square brackets 2 over 3 minus 1 half close square brackets space equals space 36 space rad.
No space of space revolution space fraction numerator 36 over denominator 2 straight pi end fraction space Less space than space 6

    Question 490
    CBSEENPH11020326

    STATEMENT – 1
    Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
    STATEMENT – 2
    Principle of conservation of momentum holds true for all kinds of collisions.

    • The statement I is True, Statement II is False.

    • The statement I is True, Statement II is True; Statement II is a correct explanation for Statement I.

    • The statement I is True, Statement II is True; Statement II is not the correct explanation for Statement I.

    • Statement I is False, Statement II is

    Solution

    B.

    The statement I is True, Statement II is True; Statement II is a correct explanation for Statement I.

    Question 491
    CBSEENPH11020334

    Two fixed frictionless inclined planes making an angle 30° and 60° with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?

    • 4.9 ms-2 in horizontal direction

    • 9.8 ms-2 in vertical direction

    • zero

    • 4.9 ms-2 in vertical direction

    Solution

    D.

    4.9 ms-2 in vertical direction

    For the motion of block along inclined plane
    mg sin θ =ma
    a = g sin θ
    where a is along the inclined plane.
    The vertical component of acceleration is g sin2θ
    Therefore, the relative vertical acceleration of  A with respect to B is 
    g (sin260 - sin230) = g/2 = 4.9 ms-2 (in vertical direction)

    Question 492
    CBSEENPH11020335

    For a particle in uniform circular motion, the acceleration an at straight a with rightwards arrow on top point P (R, θ) on the circle of radius R is (Here θ is measured from the x–axis)

    • negative straight v over straight R space cos space straight theta space bold i with bold hat on top space plus space straight v squared over straight R space sin space straight theta space bold j with bold hat on top
    • negative straight v over straight R space sin space straight theta space bold i with bold hat on top space plus space straight v squared over straight R space cos space straight theta space bold j with bold hat on top
    • negative straight v over straight R space cos space straight theta space bold i with bold hat on top space minus space straight v squared over straight R space sin space straight theta space bold j with bold hat on top
    • straight v squared over straight R space straight i with hat on top space plus fraction numerator begin display style straight v squared end style over denominator begin display style straight R end style end fraction space straight j with hat on top

    Solution

    C.

    negative straight v over straight R space cos space straight theta space bold i with bold hat on top space minus space straight v squared over straight R space sin space straight theta space bold j with bold hat on top
    straight a with rightwards arrow on top space equals space minus space straight V squared over straight R space cos space straight theta space straight i with hat on top space minus space straight V squared over straight R space sin space straight theta space straight j with hat on top

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