"Only two
things are infinite, the universe and human stupidity, and I'm not sure about
the former."

– Albert
Einstein

(1) In the system shown in the adjoining figure, the horizontal surface on which block A is placed is smooth and the pulleys are light and frictionless. If

*g =*10 ms^{–2},*the tension**T*in the string (which may be assumed to be weightless and inextensible) is
(a) 1 N

(b) 2N

(c) 5 N

The
velocity of the iron block at the moment of hitting the nail is 6 ms

^{–1}.
(d) 10 N

(e) 20 N

Net force driving the system = Weight of B =

*mg*= 2×10 = 20 N.
Acceleration (

*a*) of the system is given by*a*= Driving force /Total mass moved =

^{20}/

_{4}= 5 ms

^{–2}.

Tension,

*T*= Weight of B moving down (as in a lift) =*m*(*g*–*a*) = 2(10 – 5) =10 N.
(2) An iron block of mass 8 kg falling vertically down hits a nail on a block of wood (fig.). The
velocity of the iron block at the moment of hitting the nail is 6 ms

^{–1}. If the nail penetrates through 2 cm into the wooden block due to the impact, what is the force exerted by the iron block on the nail?
(a) 1600 N

(b) 2200 N

(c) 4800 N

(d) 7200 N

(e) 9600 N

The acceleration (in fact, retardation),

*a*of the iron block during the impact is given by
0

*=*6^{2}+ 2*a*×(0.02), from the equation*v*^{2}*=**u*^{2}+ 2*as*
This gives

*a =*– 900 ms^{–2}
The negative sign shows that the iron block is

*retarded*.
The retarding force exerted by the nail on the iron block is of magnitude

*F*given by*F = ma =*8×900 = 7200 N

The force exerted by the iron block on the nail is equal and opposite to that exerted by the nail on the iron block. The answer therefore is 7200 N.

[The above question can be modified as follows:

An iron block of mass 8 kg falling freely from rest under gravity from a height of 1.8 m hits a nail on a block of wood (fig.). If the nail penetrates through 2 cm into the wooden block due to the impact, what is the force exerted by the iron block on the nail? (

*g =*10 ms^{–2})
(a) 1600 N

(b) 2200 N

(c) 4800 N

(d) 7200 N

(e) 9600 N

The answer will be unchanged since the velocity at the moment of hitting the nail will be 6 ms

^{–1}itself (*v =*√(2*gh*) = √(2×10×1.8) = √(36) = 6)].
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