A small bug is placed between two blocks of masses M1 and M2(M1 > M2)on a frictionless horizontal table. A horizontal force f can be applied that either to M1 or M2 as shown in the figure (i) and (ii) respectively. Of these two cases the bug has a greater chance of surviving in :
A) in case (i)
B) in case (ii)
C) in both cases
D) none of these
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Answer:
A) case 1
Explanation:
The acceleration in this case will be F/(m1+m2)
normal force in case 1 will be= m2*f/m1+m2
normal force in case 2 will be= m1*f/m1+m2
as m1>m2,
normal force in case1 is smaller than normal force in case2
so the insect will have greater chance of surviving in case 1.
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The bug will have a greater chance of surviving in A) Case (i).
- Since the bug is placed between the boxes, it will experience the normal force due to the box.
- The smaller the normal force, the greater are the chances of survival for the bug.
- Let the net acceleration of the system in both cases (i) and (ii) be 'a'.
(The acceleration in both cases will be the same and equals F / M1 + M2)
- In case (i), the force F is applied on the larger box M1. The normal force developed between the boxes = N1 = M2 X a
- Similarly, in case (ii), the normal reaction N2 = M1 X a
- Since M1 > M2
⇒ M1 X a > M2 X a
⇒ N2 > N1
- Since the normal reaction is larger in case (ii), the chances of survival are greater in case (i).
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