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Physics Test 2

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Physics Test 2
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  • Question 1
    4 / -1

    If a block of mass M is floating on the water (ρw= 1000 kg/m3) with 100 cm3 volume such that 1/4th of the volume of the block is immersed in water. Find the mass of another block placed over this block such that lower block just gets immersed completely.

    Solution

    When initially 1/4th volume is immersed, writing the force equation in Y-direction; 

    V*ρblock*g= V/4 * ρw * g... (V is volume of block) 

    From this,

    ρblock= ρw/4 

    When another block is placed such that the lower block just gets fully immersed, 

    mg+ V*ρblock*g= V * ρw * g 

    from this,

    m= ( ¾)* V* ρw= 0.075 kg=75 g

     

  • Question 2
    4 / -1

    What is not true regarding Reynold’s number?

    Solution

    Reynold’s number is inversely proportional to kinematic viscosity. Because of lesser the viscosity, higher are the chances of flow being turbulent. Or flow with high-Reynold’s number.

     

  • Question 3
    4 / -1

    A 70kg man, standing on the bank of the river, suddenly jumps in a boat with mass 10kg and going with speed 10m/s (X-direction) downstream, perpendicular to its motion. The velocity of man while jumping is 2m/s (Y-direction). Find the final velocity with direction. Assume the velocities of the man (y-axis) and the boat (x-axis) are pointing in the positive direction initially.

    Solution

    Momentum conservation in X-axis, 

    Pi= Pf 

    Mman* 0 +Mboat*10 = (Mman + Mboat) * Vfx 

    Vfx= 1.25 m/s 

    Momentum conservation in Y-axis, 

    Pi= Pf 

    Mman*2 + Mboat*0 = (Mman+Mboat) * Vfy 

    Vfy= 1.75 m/s

     

  • Question 4
    4 / -1

    The upstream velocity of a boat is 2m/s and downstream velocity is 20m/s and distance between two points is 500m. What is the time required by the boat to go upstream if the river is flowing with half of the original speed?

    Solution

    For Upstream,

    Vboat – Vriver= Vupstream= 2 m/s ......(1) 

    For downstream, 

    Vboat + Vriver= Vdownstream= 20 m/s .....(2) 

    From eq.(1) and (2), 

    Vboat= 11 m/s and Vriver= 9 m/s 

    Given if Vriver(new)= 9/2= 4.5 m/s 

    Therefore,

    Vupstream= Vboat – Vriver(new)= 11 - 4.5= 6.5 m/s 

    Therefore, time required to go upstream= 500/6.5≈ 77 sec

     

  • Question 5
    4 / -1

    Which of the following is true?

    Solution

    Periodic motion has nothing to do with the path of the object whereas oscillatory motion is always periodic in nature.
    In the oscillatory motion, there is to and fro displacement of the body about a fixed point.

     

  • Question 6
    4 / -1

    For a particle performing SHM, if the maximum velocity of the particle is made 4 times, which one of the following is true?

    Solution

    Since, frequency depends on the mass and spring constant, frequency and time period won’t change. 

    Vmax = Aω 

    If Vmax is made 4 times, and frequency is constant amplitude will become 4 times. 

    Amax = Aω2 

    So frequency is constant, maximum acceleration only depends on amplitude. Hence it will become 4 times, not 8 times.

     

  • Question 7
    4 / -1

    If two balls, 2 kg and 5 kg, are separated such that their center of mass lies at the origin. If the 2 kg ball starts moving at velocity 5 m/s to the left and the 5 kg ball starts moving right with velocity 1 m/s, find the velocity and position of the center of mass after 4 sec.

    Solution

    Mtotal*Vcm= M1*V1 + M2*V2 

    V1= -5m/s and V2= +1 m/s 

    Substituting the values, 

    (2+5)*Vcm= 2*(-5)+5*(1) =-5 

    Vcm= -0.72 m/s 

    Xcm= Vcm * t= -0.72*4= -2.88 m

     

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