A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio ( sin θc/ sin θs) is :

Question

A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio ( sin θc/ sin θs) is : (A) √(8/7)  (B) √(15/14)  (C) (8/7)  (D) (15/14)

Tardigrade Admin · Accepted Answer

(g sin θc/1+(1)2)=(g sin θs/1+(2)5) ( sinθc/ sin θs)=(3/ 2/7/ 5)=(15/14)

Q. A cylinder of mass $M_{c}$ and sphere of mass $M_{s}$ are placed at points $A$ and $B$ of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio $\frac{s i n θ _{c}}{s i n θ _{s}}$ is :

$\frac{8}{7}$

$\frac{15}{14}$

$\frac{8}{7}$

$\frac{15}{14}$

$\frac{g s i n θ _{c}}{1 + \frac{1}{2}} = \frac{g s i n θ _{s}}{1 + \frac{2}{5}}$
$\frac{s i n θ _{c}}{s i n θ _{s}} = \frac{3/2}{7/5} = \frac{15}{14}$

Q. A cylinder of mass Mc​ and sphere of mass Ms​ are placed at points A and B of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio sinθs​sinθc​​ is :

78​​

1415​​

78​

1415​

1+21​gsinθc​​=1+52​gsinθs​​ sinθs​sinθc​​=7/53/2​=1415​

Q. A cylinder of mass $M_{c}$ and sphere of mass $M_{s}$ are placed at points $A$ and $B$ of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio $\frac{s i n θ _{c}}{s i n θ _{s}}$ is :

$\frac{8}{7}$

$\frac{15}{14}$

$\frac{8}{7}$

$\frac{15}{14}$

$\frac{g s i n θ _{c}}{1 + \frac{1}{2}} = \frac{g s i n θ _{s}}{1 + \frac{2}{5}}$
$\frac{s i n θ _{c}}{s i n θ _{s}} = \frac{3/2}{7/5} = \frac{15}{14}$