33(d)
a simple pendulum havin a bob of mass m is suspended 4rm d ceilin of d car used in a stunt film shootin.the car moves up along an inclined cliff at a speed v and lands at sum distance.let R be the max height of d car 4rm d top of d cliff.the tension in d string wen d car is in d aor z
a)mg b)mg-mv2/R c)mg+mv2/R d)zero
-
UP 0 DOWN 0 1 8
8 Answers
33Let angle of cliff be theta..
now by projectile we know that..
Max Height(R)=v2sin2θ/2g
also v2cos2θ/Rc=g ...Rc is different from R ..Rc is radius of curvature..
Rc= v2cos2θ/g
Rc= v2(1-sin2θ)/g...(i)
Now R=v2sin2θ/2g
v2sin2θ=2Rg.. (ii)
Putting ii in i
Rc=(v2-2Rg)/g
also from FBD of bob..
T+mv2cos2θ/Rc=mg
T=mg-mv2cos2θ/Rc
Put value of Rc
T=mg-mv2cos2θ
(v2-2Rg)/g
T=mgv2-mg2Rg-mv2cos2θg
(v2-2Rg)/g
T=(mgv2sin2θ-mg2Rg)/(v2-2Rg)/g
Put sin2θ=2Rg/v2 from ii
T=0 ans
33Also see that this is tension when bob is vertically downward... not at any extreme position... as since Rc is large as compared to thread... also angular displacement of bob is small...
β is small so cosβ taken as 1... ans is approx..