$A$ man of mass $70 \; kg$ stands on a weighing scale in a lift which is moving:
$(a)$ Upwards with a uniform speed of $10 \; m s^{-1}$.
$(b)$ Downwards with a uniform acceleration of $5 \; m s^{-2}$.
$(c)$ Upwards with a uniform acceleration of $5 \; m s^{-2}$.
What would be the readings on the scale in each case?
$(d)$ What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

(N/A) Given: Mass of the man,$m = 70 \; kg$,Acceleration due to gravity,$g = 10 \; m s^{-2}$.
$(a)$ When the lift moves upwards with a uniform speed,acceleration $a = 0$. The equation of motion is $R - mg = ma$. Since $a = 0$,$R = mg = 70 \times 10 = 700 \; N$. The reading on the scale is $700/10 = 70 \; kg$.
$(b)$ When the lift moves downwards with acceleration $a = 5 \; m s^{-2}$,the equation of motion is $mg - R = ma$,so $R = m(g - a) = 70(10 - 5) = 70 \times 5 = 350 \; N$. The reading on the scale is $350/10 = 35 \; kg$.
$(c)$ When the lift moves upwards with acceleration $a = 5 \; m s^{-2}$,the equation of motion is $R - mg = ma$,so $R = m(g + a) = 70(10 + 5) = 70 \times 15 = 1050 \; N$. The reading on the scale is $1050/10 = 105 \; kg$.
$(d)$ When the lift falls freely,$a = g$. The equation of motion is $R = m(g - g) = 0 \; N$. The reading on the scale is $0 \; kg$. The man experiences weightlessness.