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Question Number 39750 by rahul 19 last updated on 10/Jul/18

Commented by rahul 19 last updated on 10/Jul/18

Commented by rahul 19 last updated on 10/Jul/18

Also find Acc^n  of block A & D  just after the  spring 1 is cut .

$$\mathrm{Also}\:\mathrm{find}\:\mathrm{Acc}^{\mathrm{n}} \:\mathrm{of}\:\mathrm{block}\:\mathrm{A}\:\&\:\mathrm{D}\:\:\mathrm{just}\:\mathrm{after}\:\mathrm{the} \\ $$$$\mathrm{spring}\:\mathrm{1}\:\mathrm{is}\:\mathrm{cut}\:. \\ $$

Commented by rahul 19 last updated on 10/Jul/18

Mrw Sir , this Q. is waiting for u .

$$\mathrm{Mrw}\:\mathrm{Sir}\:,\:\mathrm{this}\:\mathrm{Q}.\:\mathrm{is}\:\mathrm{waiting}\:\mathrm{for}\:\mathrm{u}\:. \\ $$

Answered by MrW3 last updated on 11/Jul/18

With “after the cut of a string” I don′t mean  the instant when the string is cut.    Before a string is cut:  T_(AB) =30 N  T_(S1) =60 N  T_(S2) =20 N  T_(CD) =40 N  T_(CP) =60 N  After cut at spring 2:  a=(((6−4)g)/(6+4))=(g/5)=2 m/s^2   30−T_(AB) =3×2  ⇒T_(AB) =24 N<30 N  ⇒Q(i)⇒A(b)    T_(CD) −20=2×2  ⇒T_(CD) =24 N<40 N  ⇒Q(ii)⇒A(b)    After cut at string btw. C and pulley:  A and B have frei fall.  C,D and E have frei fall.  T_(AB) =0  T_(CD) =0  ⇒Q(iii)⇒A(d)    ⇒Q(iv)⇒A(d)

$${With}\:``{after}\:{the}\:{cut}\:{of}\:{a}\:{string}''\:{I}\:{don}'{t}\:{mean} \\ $$$${the}\:{instant}\:{when}\:{the}\:{string}\:{is}\:{cut}. \\ $$$$ \\ $$$${Before}\:{a}\:{string}\:{is}\:{cut}: \\ $$$${T}_{{AB}} =\mathrm{30}\:{N} \\ $$$${T}_{{S}\mathrm{1}} =\mathrm{60}\:{N} \\ $$$${T}_{{S}\mathrm{2}} =\mathrm{20}\:{N} \\ $$$${T}_{{CD}} =\mathrm{40}\:{N} \\ $$$${T}_{{CP}} =\mathrm{60}\:{N} \\ $$$${After}\:{cut}\:{at}\:{spring}\:\mathrm{2}: \\ $$$${a}=\frac{\left(\mathrm{6}−\mathrm{4}\right){g}}{\mathrm{6}+\mathrm{4}}=\frac{{g}}{\mathrm{5}}=\mathrm{2}\:{m}/{s}^{\mathrm{2}} \\ $$$$\mathrm{30}−{T}_{{AB}} =\mathrm{3}×\mathrm{2} \\ $$$$\Rightarrow{T}_{{AB}} =\mathrm{24}\:{N}<\mathrm{30}\:{N} \\ $$$$\Rightarrow{Q}\left({i}\right)\Rightarrow{A}\left({b}\right) \\ $$$$ \\ $$$${T}_{{CD}} −\mathrm{20}=\mathrm{2}×\mathrm{2} \\ $$$$\Rightarrow{T}_{{CD}} =\mathrm{24}\:{N}<\mathrm{40}\:{N} \\ $$$$\Rightarrow{Q}\left({ii}\right)\Rightarrow{A}\left({b}\right) \\ $$$$ \\ $$$${After}\:{cut}\:{at}\:{string}\:{btw}.\:{C}\:{and}\:{pulley}: \\ $$$${A}\:{and}\:{B}\:{have}\:{frei}\:{fall}. \\ $$$${C},{D}\:{and}\:{E}\:{have}\:{frei}\:{fall}. \\ $$$${T}_{{AB}} =\mathrm{0} \\ $$$${T}_{{CD}} =\mathrm{0} \\ $$$$\Rightarrow{Q}\left({iii}\right)\Rightarrow{A}\left({d}\right) \\ $$$$ \\ $$$$\Rightarrow{Q}\left({iv}\right)\Rightarrow{A}\left({d}\right) \\ $$

Commented by rahul 19 last updated on 13/Jul/18

Sorry sir , your ans. didn't match with book ans. Kindly check !

Commented by rahul 19 last updated on 13/Jul/18

Ans.  (i) → c  (ii)→b  (iii)→b,d  (iv)→b.

$$\mathrm{Ans}. \\ $$$$\left(\mathrm{i}\right)\:\rightarrow\:\mathrm{c} \\ $$$$\left(\mathrm{ii}\right)\rightarrow\mathrm{b} \\ $$$$\left(\mathrm{iii}\right)\rightarrow\mathrm{b},\mathrm{d} \\ $$$$\left(\mathrm{iv}\right)\rightarrow\mathrm{b}. \\ $$

Commented by MrW3 last updated on 13/Jul/18

I know. The answer depents very much  what is meant with “after ...”.  For  my answers I didn′t mean the instant  immediately after a string is cut, but  I meant the stable state after a string  is cut. In this state all objects have a  defined motion.  Please don′t take this kind of solution  from me as “correct” solution.

$${I}\:{know}.\:{The}\:{answer}\:{depents}\:{very}\:{much} \\ $$$${what}\:{is}\:{meant}\:{with}\:``{after}\:...''.\:\:{For} \\ $$$${my}\:{answers}\:{I}\:{didn}'{t}\:{mean}\:{the}\:{instant} \\ $$$${immediately}\:{after}\:{a}\:{string}\:{is}\:{cut},\:{but} \\ $$$${I}\:{meant}\:{the}\:{stable}\:{state}\:{after}\:{a}\:{string} \\ $$$${is}\:{cut}.\:{In}\:{this}\:{state}\:{all}\:{objects}\:{have}\:{a} \\ $$$${defined}\:{motion}. \\ $$$${Please}\:{don}'{t}\:{take}\:{this}\:{kind}\:{of}\:{solution} \\ $$$${from}\:{me}\:{as}\:``{correct}''\:{solution}. \\ $$

Commented by rahul 19 last updated on 13/Jul/18

Ok , Thank You Sir :−)

$$\left.\mathrm{Ok}\:,\:\mathrm{Thank}\:\mathrm{You}\:\mathrm{Sir}\::−\right) \\ $$

Answered by MrW3 last updated on 11/Jul/18

At the moment just after the spring 1  is cut:  3×10−30=3a_A   ⇒a_A =0  similarly  ⇒a_D =0

$${At}\:{the}\:{moment}\:{just}\:{after}\:{the}\:{spring}\:\mathrm{1} \\ $$$${is}\:{cut}: \\ $$$$\mathrm{3}×\mathrm{10}−\mathrm{30}=\mathrm{3}{a}_{{A}} \\ $$$$\Rightarrow{a}_{{A}} =\mathrm{0} \\ $$$${similarly} \\ $$$$\Rightarrow{a}_{{D}} =\mathrm{0} \\ $$

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