General
Easy
Physics-

A particle originally at a rest at the highest point of a smooth circle in a vertical plane, is gently pushed and starts sliding along the circle. It will leave the circle at a vertical distance h below the highest point such that

Physics-General

  1. h equals R    
  2. h equals fraction numerator R over denominator 3 end fraction    
  3. h equals fraction numerator R over denominator 2 end fraction    
  4. h equals 2 R    

    Answer:The correct answer is: h equals fraction numerator R over denominator 3 end fractionFrom law of conservation of energy, potential energy of fall gets converted to kinetic energy.

    therefore blank P E equals K E
    m g h equals fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent
    o r blank v equals square root of 2 g h end root blank open parentheses i close parentheses
    Also, the horizontal component of force is equal centrifugal force.
    therefore blank m g cos invisible function application theta equals fraction numerator m v to the power of 2 end exponent over denominator R end fraction open parentheses i i close parentheses
    From Eq. (i)
    therefore blank m g cos invisible function application theta equals fraction numerator 2 m g h over denominator R end fraction blank open parentheses i i i close parentheses
    From increment A O B comma
    cos invisible function application theta equals fraction numerator left parenthesis R minus h over denominator R end fraction
    ⟹ m g open parentheses fraction numerator open parentheses R minus h close parentheses over denominator R end fraction close parentheses equals fraction numerator 2 m g h over denominator R end fraction
    ⟹ blank 3 h equals R
    ⟹ h equals fraction numerator R over denominator 3 end fraction

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    A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at A is

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    Vertical component at A equals 2 square root of g sin invisible function application 30 degree equals square root of g

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    What is ‘A’ in the following reaction?

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    Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is v subscript 0 end subscript, then the ratio of tensions in the three sections of the string is

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    physics-General
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    physics-General
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    physics-

    An aero plane moving horizontally at a speed of 200 blank m divided by s and at a height of 8.0 cross times 10 to the power of 3 end exponent blank m is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released

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    An aero plane moving horizontally at a speed of 200 blank m divided by s and at a height of 8.0 cross times 10 to the power of 3 end exponent blank m is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released

    physics-General
    Horizontal distance travelled by the bomb S equals u cross times t
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    General
    physics-

    A weightless thread can bear tension up to3.7 blank k g wt. A stone of mass 500 blank g m s is tied to it and revolved in a circular path of radius 4 blank m in a vertical plane. If g equals 10 blank m s to the power of negative 2 end exponent , then the maximum angular velocity of the stone will be

    Max. tension that string can bear equals 3.7 blank k g w t equals 37 blank N
    Tension at lowest point of vertical loop equals m g plus m omega to the power of 2 end exponent r
    equals 0.5 cross times 10 plus 0.5 cross times omega to the power of 2 end exponent cross times 4 equals 5 plus 2 omega to the power of 2 end exponent
    therefore 37 equals 5 plus 2 omega to the power of 2 end exponent rightwards double arrow omega equals 4 blank r a d divided by s

    A weightless thread can bear tension up to3.7 blank k g wt. A stone of mass 500 blank g m s is tied to it and revolved in a circular path of radius 4 blank m in a vertical plane. If g equals 10 blank m s to the power of negative 2 end exponent , then the maximum angular velocity of the stone will be

    physics-General
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    Tension at lowest point of vertical loop equals m g plus m omega to the power of 2 end exponent r
    equals 0.5 cross times 10 plus 0.5 cross times omega to the power of 2 end exponent cross times 4 equals 5 plus 2 omega to the power of 2 end exponent
    therefore 37 equals 5 plus 2 omega to the power of 2 end exponent rightwards double arrow omega equals 4 blank r a d divided by s