question_answer

                A mass of 1 kg is suspended by a thread. It is                 (i) lifted up with an acceleration \[4.9\,m/{{s}^{2}},\]                 (ii) lowered with an acceleration \[4.9\,m/{{s}^{2}}\].                 The ratio of the tensions is:                                                                        

A)                            3 : 1 

B)                 1 : 3       

C)                                            1 : 2   

D)                                            2 : 1

Correct Answer: A

Solution :

                                          Key Idea : In a lift weight is the net force acting on the mass while going upwards or downwards. (i) When mass is lifted upwards with an acceleration a, then apparent weight.                                            \[{{T}_{1}}-mg=ma\]                 \[\Rightarrow {{T}_{1}}=mg+ma\]                 \[{{T}_{1}}=m(g+a)\]                 Substituting the values, we obtain                 \[\therefore {{T}_{1}}=(1)\,(9.8+4.9)=14.7\,V\]                 (ii) When mass is lowered downwards with an acceleration a, then                                 \[mg-{{T}_{2}}=ma\]                 \[\Rightarrow \,\,{{T}_{2}}=mg-ma=m(g-a)\]                 Substituting the values, we have                 \[{{T}_{2}}=(1)\,(9.8-4.9)\,=4.9\,N\]                 Then, ratio of tensions                 \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{14.7}{4.9}=\frac{3}{1}\]                 \[\Rightarrow \]               \[{{T}_{1}}:{{T}_{2}}=3:1\]