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Himanshu Dogra Grade: 11
        

Please solve the questions given in the photograph from FIITJEE AITS.


1392_28768_25022011015.jpg

6 years ago

Answers : (4)

vikas askiitian expert
510 Points
										

just after first collision let velociy of bob is v then


 


applying momentam conservation


 


initial momantam of system(Pi) = (m/2) (u)


 u = (2gL)1/2 so Pi = m(2gL)1/2/2


final momemtam (Pf) = mv


 mv = m(2gL)1/2 /2                          (from momentam conservation)


   v = (gL/2)1/2             ................1


KE of bob is mv2/2


KE = mgL/4      ...............2


when bob is at max height then its KE is converted into PE


 mgL/4 = mgHmax


   L/4 = Hmax     


from floor height of bob is L+Hmax = L/4+L = 5L/4                                  (Q15 => option c)

6 years ago
vikas askiitian expert
510 Points
										

let tension in string just after collision is T then


 


T - mg = mv2/r (centripital force)                                         { tension is in upward direction , weight is in downward direction }


 


T = mg + mv2/L


 


v = (gL/2)1/2  so


 


T = 3mg/2               (ans14 =>c )

6 years ago
vikas askiitian expert
510 Points
										

just after second collision , let velocity of bob is v1 & tension in string is T ...


 


after collision this system becomes conical pendulam so verticle component of tension is balanced by weight &


centripital force is provided by horizontal component of tension ...


 


let string makes an angle of @ with verticle then


 


Tcos@ = weight = 2mg       ............1      (weight of bob + particle)


 


Tsin@ = 2mv12 /r              .............2        (r is radius of its path)


r = Lsin@         .........3


from 1,2 & 3


 


v12 = {gLsin@tan@}                  ..................4


 


time period of this system = T = 2pir/v1


                                           = 2pi(Lsin@)/{gLsin@tan@}1/2           ........................5


now , @ can be calculated by using trignometry ... height of this cone = L - L/4 = 3L/4


                                                                      slant height = L


              cos@ = 3/4


so , time perion will be T = 2pi(3L/4g)1/2

6 years ago
vikas askiitian expert
510 Points
										

approve if u like my ans

6 years ago
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