A) \[{{h}^{1/3}}{{G}^{2/3}}{{c}^{1/3}}{{A}^{1}}\]
B) \[{{h}^{2/3}}{{c}^{5/3}}{{G}^{1/3}}{{A}^{1}}\]
C) \[{{h}^{2/3}}{{c}^{1/3}}{{G}^{4/3}}{{A}^{1}}\]
D) \[{{h}^{2}}{{G}^{3/2}}{{c}^{1/3}}{{A}^{1}}\]
Correct Answer: A , B , C , D
Solution :
NOTE: (No option is correct) Bonus Stopping potential \[\left( V \right)\propto {{h}^{x}}{{I}^{y}}{{G}^{z}}{{C}^{r}}\] Here, h = plank?s constant \[=\left[ M{{L}^{2}}{{T}^{1}} \right]\] \[I=current=\left[ A \right]\] G = Gravitational constant \[=\left[ {{M}^{1}}{{L}^{3}}{{T}^{2}} \right]\] and c = speed of light \[=\left[ L{{T}^{1}} \right]\] \[\therefore \] and V = potential \[=\left[ M{{L}^{2}}{{T}^{3}}{{A}^{1}} \right]\] \[\therefore \left[ M{{L}^{2}}{{T}^{3}}{{A}^{1}} \right]={{\left[ M{{L}^{2}}{{T}^{1}} \right]}^{x}}{{\left[ A \right]}^{y}}{{\left[ {{M}^{1}}{{L}^{3}}{{T}^{2}} \right]}^{z}}\text{ }{{\left[ L{{T}^{1}} \right]}^{r}}\]Comparing dimension of M, L, T, A, we get \[y=1,x=0,z=1,r=5\] \[\therefore \]Solution :
NOTE: (No option is correct) Bonus Stopping potential \[\left( V \right)\propto {{h}^{x}}{{I}^{y}}{{G}^{z}}{{C}^{r}}\] Here, h = plank?s constant \[=\left[ M{{L}^{2}}{{T}^{1}} \right]\] \[I=current=\left[ A \right]\] G = Gravitational constant \[=\left[ {{M}^{1}}{{L}^{3}}{{T}^{2}} \right]\] and c = speed of light \[=\left[ L{{T}^{1}} \right]\] \[\therefore \] and V = potential \[=\left[ M{{L}^{2}}{{T}^{3}}{{A}^{1}} \right]\] \[\therefore \left[ M{{L}^{2}}{{T}^{3}}{{A}^{1}} \right]={{\left[ M{{L}^{2}}{{T}^{1}} \right]}^{x}}{{\left[ A \right]}^{y}}{{\left[ {{M}^{1}}{{L}^{3}}{{T}^{2}} \right]}^{z}}\text{ }{{\left[ L{{T}^{1}} \right]}^{r}}\]Comparing dimension of M, L, T, A, we get \[y=1,x=0,z=1,r=5\] \[\therefore \]Solution :
NOTE: (No option is correct) Bonus Stopping potential \[\left( V \right)\propto {{h}^{x}}{{I}^{y}}{{G}^{z}}{{C}^{r}}\] Here, h = plank?s constant \[=\left[ M{{L}^{2}}{{T}^{1}} \right]\] \[I=current=\left[ A \right]\] G = Gravitational constant \[=\left[ {{M}^{1}}{{L}^{3}}{{T}^{2}} \right]\] and c = speed of light \[=\left[ L{{T}^{1}} \right]\] \[\therefore \] and V = potential \[=\left[ M{{L}^{2}}{{T}^{3}}{{A}^{1}} \right]\] \[\therefore \left[ M{{L}^{2}}{{T}^{3}}{{A}^{1}} \right]={{\left[ M{{L}^{2}}{{T}^{1}} \right]}^{x}}{{\left[ A \right]}^{y}}{{\left[ {{M}^{1}}{{L}^{3}}{{T}^{2}} \right]}^{z}}\text{ }{{\left[ L{{T}^{1}} \right]}^{r}}\]Comparing dimension of M, L, T, A, we get \[y=1,x=0,z=1,r=5\] \[\therefore \]Solution :
NOTE: (No option is correct) Bonus Stopping potential \[\left( V \right)\propto {{h}^{x}}{{I}^{y}}{{G}^{z}}{{C}^{r}}\] Here, h = plank?s constant \[=\left[ M{{L}^{2}}{{T}^{1}} \right]\] \[I=current=\left[ A \right]\] G = Gravitational constant \[=\left[ {{M}^{1}}{{L}^{3}}{{T}^{2}} \right]\] and c = speed of light \[=\left[ L{{T}^{1}} \right]\] \[\therefore \] and V = potential \[=\left[ M{{L}^{2}}{{T}^{3}}{{A}^{1}} \right]\] \[\therefore \left[ M{{L}^{2}}{{T}^{3}}{{A}^{1}} \right]={{\left[ M{{L}^{2}}{{T}^{1}} \right]}^{x}}{{\left[ A \right]}^{y}}{{\left[ {{M}^{1}}{{L}^{3}}{{T}^{2}} \right]}^{z}}\text{ }{{\left[ L{{T}^{1}} \right]}^{r}}\]Comparing dimension of M, L, T, A, we get \[y=1,x=0,z=1,r=5\] \[\therefore \]
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