A block of mass m, is kept on a wedge of mass M, as shown in figure such that mass m remains stationary w.r.t. wedge. The magnitude of force P is

Question

A block of mass m, is kept on a wedge of mass M, as shown in figure such that mass m remains stationary w.r.t. wedge. The magnitude of force P is (A) g tan β (B) m g tan β (C) (m+M) g tan β (D) m g cot β

Tardigrade Admin · Accepted Answer

If acceleration of the system is a then

P = (M + m) a

from the reference frame of wedge
Component of

ma

along the inclined will be ma cos

β

for the block to be in equilibrium w.r.t. wedge

ma cos β = m g sin β

a = g tan β

hence

P = (M + m) g tan β

Q. A block of mass $m$ , is kept on a wedge of mass $M$ , as shown in figure such that mass $m$ remains stationary w.r.t. wedge. The magnitude of force $P$ is

$g tan β$

$m g tan β$

$(m + M) g tan β$

$m g cot β$

If acceleration of the system is a then $P = (M + m) a$
from the reference frame of wedge
Component of $ma$ along the inclined will be ma cos $β$ for the block to be in equilibrium w.r.t. wedge
$ma cos β = m g sin β$
$a = g tan β$
hence $P = (M + m) g tan β$

Q. A block of mass m, is kept on a wedge of mass M, as shown in figure such that mass m remains stationary w.r.t. wedge. The magnitude of force P is

gtanβ

mgtanβ

(m+M)gtanβ

mgcotβ