Question

A block of wood is kept on the table top. The mass of wooden block is $5 \mathrm{kg}$ and its dimensions are $40 \mathrm{cm} \times 20 \mathrm{cm} \times 10 \mathrm{cm} .$ Find the pressure exerted by the wooden
block on the table top, if it is made to lie on the table top with its sides of dimensions (a) $20 \mathrm{cm} \times 10 \mathrm{cm}$ and $(\mathrm{b}) 40 \mathrm{cm} \times 20 \mathrm{cm}$
A (a)$P=2440 N m^{-2}$ (b) $P=610.5 N m^{-2}$
B (a)$P=2450 \mathrm{Nm}^{-2}$ (b) $\mathrm{P}=612.5 \mathrm{Nm}^{-2}$
C (a)$P=2460 N m^{-2}$ (b) $P=618.5 N m^{-2}$
D (a)$P=2470 N m^{-2}$ (b) $P=712.5 N m^{-2}$

Answer 1

Hint: We should know that velocity is defined as the rate change of displacement per unit time. Speed in a specific direction is also known as velocity. Velocity is equal to displacement divided by time. Speed, being a scalar quantity, is the rate at which an object covers distance. The average speed is the distance which is a scalar quantity per time ratio. On the other hand, velocity is a vector quantity; it is direction-aware. An object which moves in the negative direction has a negative velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion in this case. Based on this we have to solve this question.

Complete step by step answer
From the data given in the question,
We see that,
Mass of the wooden block, $\mathrm{m}=5 \mathrm{kg}$
Thrust due to wooden block, $\mathrm{Mg}=5 \mathrm{kg} \times 9.8 \mathrm{ms}^{-2}=49 \mathrm{N}$
(a) Surface area of $20 \mathrm{cm} \times 10 \mathrm{cm}$ surface,
$\mathrm{A}=(20 \times 10) \mathrm{cm}^{2}$
$=(0.2 \times 0.1) \mathrm{m}^{2}$
$=0.02 \mathrm{m}^{2}$
$P=\dfrac{m g}{A}$
With the given equation, we can derive,
$\mathrm{P}=\dfrac{49 \mathrm{N}}{0.02 \mathrm{m}^{2}}=\dfrac{49}{0.02} \mathrm{Nm}^{-2}$
or Pressure, $\mathrm{P}=2450 \mathrm{Nm}^{-2}$.
(b) Surface area of $40 \mathrm{cm} \times 20 \mathrm{cm}$ surface,
$\mathrm{A}=(40 \times 20) \mathrm{cm}^{2}$
$=(0.4 \times 0.2) \mathrm{m}^{2}=0.08 \mathrm{m}^{2}$
Equating from the derived data, we get,
$\mathrm{P}=\dfrac{49 \mathrm{N}}{0.08 \mathrm{m}^{2}}=\dfrac{49}{0.08} \mathrm{Nm}^{-2}$
or Pressure, $P=612.5 \mathrm{Nm}^{-2}$

Therefore, the correct answer is Option B.

Note: We should know that if an object's speed or velocity is increasing at a constant rate then we say it has uniform acceleration. The rate of acceleration is constant. If a car speeds up then slows down then speeds up it doesn't have uniform acceleration. The instantaneous acceleration, or simply acceleration, is defined as the limit of the average acceleration when the interval of time considered approaches 0. It is also defined in a similar manner as the derivative of velocity with respect to time. If an object begins acceleration from rest or a standstill, its initial time is 0. If we get a negative value for acceleration, it means the object is slowing down. The acceleration of an object is its change in velocity over an increment of time. This can mean a change in the object's speed or direction. Average acceleration is the change of velocity over a period of time. Constant or uniform acceleration is when the velocity changes the same amount in every equal time period.