A conducting wire is stretched by applying a deforming force, so that its diameter decreases to 40% of the original value. The percentage change in its resistance will be:
Step 1: {Analyze the impact of stretching}
As the wire's volume is constant, the relationship \( V = A l \) applies, where \(A\) denotes the cross-sectional area and \(l\) represents the length.
Step 2: {Calculate the updated resistance}
The resistance formula is: \[ R = \rho \frac{l}{A} \] Given that \(A\) is inversely proportional to \(d^2\) and \(l\) increases proportionally, the change in resistance is described by: \[ \frac{\Delta R}{R} = -4 \frac{\Delta D}{D} \] With \(\Delta D = -0.4\), the calculation is: \[ \frac{\Delta R}{R} = -4(-0.4) = 1.6\% \] Therefore, the resistance experiences a \(1.6\%\) increase.
A metal plate of area 10-2m2 rests on a layer of castor oil, 2 × 10-3m thick, whose viscosity coefficient is 1.55 Ns/m2. The approximate horizontal force required to move the plate with a uniform speed of 3 × 10-2ms-1 is: