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KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    A spherical steel ball released at the top of a long column of glycerine of length L, falls through a distance L/2 with accelerated motion and the remaining distance L/2 with a uniform velocity. If \[{{t}_{1}}\] and \[{{t}_{2}}\] denote the times taken to cover the first and second half and \[{{W}_{1}}\] and \[{{W}_{2}}\] the work done against gravity in the two halves, then

    A) \[{{t}_{1}}<{{t}_{2}};{{W}_{1}}>{{W}_{2}}\] 

    B) \[{{t}_{1}}>{{t}_{2}};{{W}_{1}}<{{W}_{2}}\]

    C) \[{{t}_{1}}={{t}_{2}};{{W}_{1}}={{W}_{2}}\]

    D) \[{{t}_{1}}>{{t}_{2}};{{W}_{1}}={{W}_{2}}\]

    Correct Answer: D

    Solution :

    The average velocity in the first half of the distance \[=\frac{0+v}{2}=\frac{v}{2};\] while in the second half, the average velocity is v. therefore,\[{{t}_{1}}>{{t}_{2}}\]. The work done against gravity in both halves =\[mgh=mgL/2\]. Hence the correct choice is [D].


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