Question

2. A block of mass 2kg is moving with an acceleration of 1 m/s^2 under the action of a
constant horizontal force as shown in figure. A similar
block of mass 2kg is gently glued over the moving block
and the two blocks are now moving as a single unit. Find
the acceleration of the combination if the same force
continuous to act.
a) 0.2m/s2
b) 0.1m/s2
c) 0.5m/s2
d) 1m/s2​

Answer 1

Answer:

$\bigstar{\bold{Option\:C:0.5\:m/s^{2}}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Initial mass of the block (m)= 2 kg
• Initial acceleration of the block = 1 m/s²
• Mass of the two block (M) = 2 + 2 = 4 kg
• Force on the initial block = Force on the two block

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Acceleration on the combination of the blocks

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First we have to find the force acting on the block initially.

→ By the second law of motion we know that,

  F = m a

  where F is the force, m is the mass and a is the acceleration

→ Substituting the data we get,

  F =  2 × 1

  F = 2 N

→ Hence force acting on the block initially is 2 N

→ By given we know that

  Force acting on the block = Force acting on the two blocks

→ Hence,

  Force acting on the two block = 2 N

→ Now we have to find the acceleration acting on this combination

→ Again by Newton's second law,

  F = m a

→ Substituting the data we get the value of acceleration,

  2 = 4 × a

  a = 2/4

  a = 0.5 m/s²

→ Hence the acceleration of the combination of the block is 0.5 m/s²

$\boxed{\bold{Acceleration=0.5\:m/s^{2} }}$

→ Hence option C is correct.

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Newton's second law state that the rate of change of momentum is directly proportional to the force applied and the change takes place in the direction of force.

 F = m a