WBJEE 2024 Physics & Chemistry Paper

To determine the horizontal force required to move the metal plate with a uniform speed, we can use the formula for viscous force, which is given by:
F=η⋅A⋅‌

v

d

where:
η is the coefficient of viscosity (given as 1.55‌Ns‌m−2 ).
A is the area of the metal plate (given as 10−2m2 ).
v is the uniform speed of the plate (given as 3×10−2ms−1 ).
d is the thickness of the castor oil layer (given as 2×10−3m ).
Substituting the given values into the formula, we get:

F=1.55⋅10−2⋅‌

3×10−2

2×10−3

First, handle the fraction:
‌

3×10−2

2×10−3

=‌

3

2

×101=1.5×10

Now, substitute this back into the equation for the force:
F=1.55⋅10−2⋅15=1.55⋅0.15
Finally, calculate the force:
F=0.2325N
Therefore, the approximate horizontal force required to move the plate with a uniform speed is:
Option B: 0.2325 N