Q.

Match the following            

 Column-I Column-II
ACube of mass m and density σ is pulled by a force Fx=mgi^ in an accelerating liquid of density ρ . The value of axay  cube is                               Question Image                                    Pρσ
B

The sphere of mass m is pulled horizontally by force  Fx = mg  in non – accelerating liquid. The value of  axay  of sphere  is 

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                  Question Image 

Q1:1
C

A closed cube of length x is placed in a rotating liquid. The value of ax/g, (where  ax  is the horizontal acceleration of the cube ) is

Question Image

   Question Image

Rσρσ
D

The string of a pendulum makes an angle θ with vertical when  the cart moves with an acceleration a. If the cart is filled with liquid of density ρ<σ  (density of the bob), the value of the angle of inclination with vertical becomes θ1 then   tanθtanθ1                     

Question Image
S2σ+ρ2(σρ)

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a

a q, b p, c s, d r     

b

a r, bq, c s, d p

c

ap, bs, cq, dr              

d

a s, b r, c p, d q     

answer is C.

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Detailed Solution

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A)   FB=ρ(mσ)geff=m(ρσ)a2+g2

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FBC of cube w.r.t container

So, cosθ=ga2+g2 and sinθ=aa2+g2

Let   ax= acc of cube w.r.t container in x-direction mg+FBsinθmg2=max

ax1=g2+ρσaax1=g2+ρσ.g2 Hence, ax1=g2+ρσaax1=g2+ρσ.g2

 In Y-direction :  

FBcosθmg=may m(ρσ)a2+g2ga2+g2mg=may

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FBD for sphere 

ay=g[ρσ1]=g[ρσ]axay=(2σ+ρ)2(ρσ)            

B)  ax=g

  ay=mg+m(ρσ)gm=(ρσσ)g axay=σρσ        

C)  (P1P2)A=m ax

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FBD of cylinder        

ρω22 [(2x)2x2]A=m ax ρ2(2g3x)3x2A=(Ax)σaxaxg=ρσ          

D)  When cart is not filled with liquid, tanθ=ag

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FBD of pendulum   

When cart is filled with liquidCart:(T+FB)sinθ1=ma   (1)     tanθ1=ag     .(2) (FB+T)cosθ1=mg  ..(3)   tanθ1tanθ=11=θ1θ=11

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