Laws of Motion

  • Question 557
    CBSEENPH11020851

    Which one of the following statements is incorrect?

    • Rolling friction is smaller than sliding friction.

    • Limiting value of static friction is directly proportional to normal reaction.

    • Coefficient of sliding friction has dimensions of length.

    • Frictional force opposes the relative motion.

    Solution

    C.

    Coefficient of sliding friction has dimensions of length.

    Coefficient of friction or sliding friction has no dimension.

    f = μsN μs = fN = [M0L0T0]

    Question 558
    CBSEENPH11020852

    A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be

    • 0.5

    • 0.25

    • 0.4

    • 0.8

    Solution

    B.

    0.25

    According to law of conservation of linear momentum,

    mv + 4m x 0 = 4mv' + 0

    v' = v4e = relative velocity of separation Relative velocity of approach =v4ve = 14 = 0.25

    Question 559
    CBSEENPH11020853

    A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and θ for the block to remain stationary on the wedge is

    • a = gcosec θ

    • a= gsin θ

    • a = g tan θ

    • a = g cos θ

    Solution

    C.

    a = g tan θ

    In non-inertial frame,

    N sin θ = ma ...(i)
    N cos θ = mg... (ii)

    tan θ = a/g
    a = g tan θ

    Question 560
    CBSEENPH11020859

    A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is p0 and temperature is T0, atmospheric pressure is also p0. Now, the temperature of the gas is increased to 2T0, the tension of the wire will be

    • 2p0A

    • p0A

    • p0A/2

    • 4p0A

    Solution

    B.

    p0A

    The volume of the gas is constant i.e., V = constant

    ∴ p ∝ T i.e pressure will be doubled if the temperature is doubled.

    Let F be the tension in the wire. Then, the equilibrium of anyone pipes gives.

    F = (p-p0) A = 2(p0 - p0) = p0A

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