Question

What force should be applied on the wedge so that block over it does not move? (All surfaces are smooth)
(1) F = (M + m) g cot ∅
(3) F = (M + m) g sin ∅
(2) F = (M + m) g tan ∅
(4) F = (M + m) g cos∅​

Answer 1

Answer:

$(3) F=(M+m)gtan(\theta)$

Explanation:

1) We know,

Acceleration of system,

$F=(m+M)a\\ \\=>a=\frac{F}{m+M}$

2) Then,

Applying pseudo force on m,= ma

Force Balance for 'm' to be at rest.

$N sin(\theta)=ma$

$Ncos(\theta)=mg$

Dividing above equations,

we get,

$a=gtan(\theta)\\ \\=>\frac{F}{m+M}= gtan(\theta)\\ \\=>F=(m+M)gtan(\theta)$

Hence, option (2) is correct option.

Answer 2

Answer:

for answer view the picture