Question # In the system shown in figure all surfaces are smooth. Rod is moved by external agent with acceleration ( 9 mathrm{m} / mathrm{s}^{2} ) vertically downwards. Force exerted on the rod by the wedge will be:

# In the system shown in figure all surfaces are smooth. Rod is moved by external agent with acceleration ( 9 mathrm{m} / mathrm{s}^{2} ) vertically downwards. Force exerted on the rod by the wedge will be:

(a) ( 120 mathrm{N} )

(b) ( 200 mathrm{N} )

(c) ( 160 mathrm{N} )

(d) ( 180 mathrm{N} )

Solution

Here ( x ) is the horizontal displacement of wedge and ( y ) is the vertical displacement of the rod.

From the figure ( tan (A)=Y / X )

i.e is ( Y=x ) tan ( A )

( a=A_{x} ) tan ( A ldots ldots ldots ldots ldots . ) Where ( A x ) is the horizontal acc of the wedge and Ay is the bvertical acc of the rod.

Now frm the wedge,

( mathrm{Nsin} mathrm{A}=mathrm{M} mathrm{A}_{mathrm{x}} )

but ( mathrm{A}_{mathrm{x}}=mathrm{a} / tan mathrm{A} )

Therefore, ( mathrm{N} sin mathrm{A}=mathrm{M} mathrm{a} / tan mathrm{A} )

On putting the values we get ( N=200 ).