91影视

a) Given:

Drag force experienced by sphere in liquid $F_{drag}=bv$

Radius of the sphere $=R$

$b=6蟺nR$

Initial speed of sphere $v_i=v_o$$v_i=v_o$

We need to determine the velocity of sphere with Time . As there is no other force except drag force in $x$direction hence its velocity will be affected by drag force only. Also the drag force is opposite to the direction of motion, hence it will lead to decrease in speed with time.

To find speed variations with time we proceed as follow:

$ma=-F_{drag}$

$a=\frac{-F_{drag}}{m}$

$F_{drag}=6蟺畏Rv$

$鉄�a=\frac{6蟺畏Rv}{m}$

Using equation of motion:

$v_f=v_i+a螖t$

$v_f=v_o-\frac{6蟺畏Rv}{m}t$

$\text{Hence}v\left(t\right)=v_o-\frac{6蟺畏Rv}{m}t$

b) Given

The coefficient of viscosity$畏=1脳{10}^{-}3\mathrm{Ns}/{\mathrm{m}}^2$

Diameter $d=4\mathrm{cm}$

$R=2\mathrm{cm}=0.02\mathrm{m}$

Mass $m=33\mathrm{g}=0.033\mathrm{Kg}$

To determine the time taken by sphere to reach $50\%$of initial speed.

Using the result of (a)

$v_f=v_o-\frac{6蟺畏Rv}{m}t$

$0.5v_o=v_o-\frac{6脳蟺脳1.0脳{10}^{-3}脳0.02脳0.5v}{0.033}t$

$f0.5\backslash \mathrm{not}p=f\frac{6脳蟺脳1.0脳{10}^{-3}脳0.02脳0.5\backslash \mathrm{not}x}{0.033}t$

$t=87.57\mathrm{s}=1.46\min$