Question 191: Centre of Mass and Rotational Motion

Question

A body of mass 1 kg falls freely from a height of 100 m, on a platform mass 3 kg which is mounted on a spring having spring constant k = 1.25 $$ 	imes $$ 10
6
N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms
–2
, the value of x will be close to :

Accepted Answer

velocity of 1 kg block just before it collides with 3kg block
= $$\sqrt {2gh}  = \sqrt {2000} $$ m/s
Applying momentum conversation just before and just after collision.
1 $$ 	imes $$ $$\sqrt {2000} $$ = 4v $$ \Rightarrow $$ v = $${{\sqrt {2000} } \over 4}$$ m/s
initial compression of spring
1.25 $$ 	imes $$ 10
6
x
0
= 30 $$ \Rightarrow $$ x
0
$$ \approx $$ 0
applying work energy theorem,
W
g
+ W
sp
= $$\Delta $$KE
$$ \Rightarrow $$    40 $$ 	imes $$ x + $${1 \over 2}$$ $$ 	imes $$ 1.25 $$ 	imes $$ 10
6
(0
2
$$-$$ x
2
)
= 0 $$-$$ $${1 \over 2}$$ $$ 	imes $$ 4 $$ 	imes $$ v
2
solving x $$ \approx $$ 4 cm

Answer

8 cm

Answer

4 cm

Answer

40 cm

Answer

80 cm

Centre of Mass and Rotational Motion

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