Question
A $$20\,kg$$ block $$B$$ is suspended from a cord attached to a $$40\,kg$$ cart $$A.$$ Find the ratio of the acceleration of block in cases (i) and (ii) shown in the figure immediately after the system is released from rest. (neglect friction)
A $$20\,kg$$ block $$B$$ is suspended from a cord attached to a $$40\,kg$$ cart $$A.$$ Find the ratio of the acceleration of block in cases (i) and (ii) shown in the figure immediately after the system is released from rest. (neglect friction)
A.
$$\frac{{\sqrt 2 }}{3}$$
B.
$$3\sqrt 2 $$
C.
$$\frac{3}{2}$$
D.
$$\frac{3}{{2\sqrt 2 }}$$
Answer :
$$\frac{3}{{2\sqrt 2 }}$$
Solution :
Case I:
$$\eqalign{ & T - N = 40\,a \cr & {\text{and}}\,\,20g - T = 20\,a \cr & {\text{Also}}\,\,N = 20\,a \cr} $$
After simplifying, we get
$$a = \frac{g}{4}$$
Acceleration of block $$B,$$ $$ = \sqrt 2 a = \frac{g}{{2\sqrt 2 }}.$$
Case II :
$$\eqalign{ & T = 40\,a \cr & {\text{and}}\,20\,g - T = 20\,a \cr} $$
After simplifying above equation, we get $$a = \frac{g}{3}$$
Ratio $$ = \frac{{\frac{g}{{2\sqrt 2 }}}}{{\frac{g}{3}}} = \frac{3}{{2\sqrt 2 }}$$
Case I:
$$\eqalign{ & T - N = 40\,a \cr & {\text{and}}\,\,20g - T = 20\,a \cr & {\text{Also}}\,\,N = 20\,a \cr} $$
After simplifying, we get
$$a = \frac{g}{4}$$
Acceleration of block $$B,$$ $$ = \sqrt 2 a = \frac{g}{{2\sqrt 2 }}.$$
Case II :
$$\eqalign{ & T = 40\,a \cr & {\text{and}}\,20\,g - T = 20\,a \cr} $$
After simplifying above equation, we get $$a = \frac{g}{3}$$
Ratio $$ = \frac{{\frac{g}{{2\sqrt 2 }}}}{{\frac{g}{3}}} = \frac{3}{{2\sqrt 2 }}$$
