Question

Four identical blocks each of mass m are placed on the top of the trolley of mass M as shown in the figure. When the horizontal force of magnitude F is applied to the trolley, it experiences an acceleration a.

If one of the blocks picked gently from the trolley while F is still being applied, the trolley will then accelerate at [M and m always move together]

$

  1)\,\left( {\dfrac{{M - 4m}}{{M + 3m}}} \right)a \\

  2)\;\left( {\dfrac{{M + 4m}}{{M + 3m}}} \right)a \\

  3){\text{ }}\left( {\dfrac{M}{{3m}}} \right)a \\

  4){\text{ }}\left( {\dfrac{M}{{3m + M}}} \right)a \\

 $

Answer 1

Hint: Always check the given terms and the format asked in the solution use the basic formula of the force and substitute in the second equation of the force and simplify for the required answer. Force is the product of mass into acceleration and is measured in kilogram into metre per Second Square and its SI (system international) unit is Newton.

Complete step by step answer:
Let the Mass of the trolley be \[ = M\]
Mass of the identical block be $ = m$
Now, the total mass of the trolley and the four blocks $ = 4m + M$
By the definition – We know that the force is the product of mass into acceleration.
$F = m \times a$
But here, $m = 4m + M$
$ \Rightarrow F = (4m + M)a{\text{ }}........{\text{(1)}}$
If one of the blocks picked gently from the trolley while F is still being applied, the trolley will then accelerate at –
$a' = \dfrac{F}{m}$
Place the value of “F” from the equation $(1){\text{ and here m = 3m + M}}$ (since one block is picked)
$
  \therefore a' = \dfrac{{(4m + M)a}}{{(3m + M)}} \\
  \therefore a' = \left( {\dfrac{{M + 4m}}{{M + 3m}}} \right)a \\
 $
Hence, from the given multiple choices- second option is the correct answer.

Note:First implementation of the correct formula is very important and its substitution for the value of mass rest goes well then. Force is the push and the pull on an object. Since its magnitude and direction both are important it is the vector quantity.