Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force P is applied to the system as shown in figure such that the mass m remains stationary with respect to block of mass M, then the magnitude of the force P is

Question

Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force P is applied to the system as shown in figure such that the mass m remains stationary with respect to block of mass M, then the magnitude of the force P is (A) (M+ m) g tan β (B) g tan β (C) m g cos β (D) (M +m) g textcosec β

Tardigrade Admin · Accepted Answer

The free body diagram of the given situation is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/896ee713888533e41bd2ee84ba2befcb-.png" /> Force = Mass × Acceleration (given) ∴ P=(M+ m) a m a cos β=m g sin β ⇒ a=g ( sin β/ cos β) =g tan β ∴ P=(M+ m) g tan β

Q. Two wooden blocks of masses $M$ and $m$ are placed on a smooth horizontal surface as shown in figure. If a force $P$ is applied to the system as shown in figure such that the mass $m$ remains stationary with respect to block of mass $M$ , then the magnitude of the force $P$ is

$(M + m) g tan β$

$g tan β$

$m g cos β$

$(M + m) g cosec β$

The free body diagram of the given situation is

Force $=$ Mass $\times$ Acceleration (given)
$∴ P = (M + m) a$
$ma cos β = m g sin β$
$\Rightarrow a = g \frac{s i n β}{c o s β}$
$= g tan β$
$∴ P = (M + m) g tan β$

Q. Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force P is applied to the system as shown in figure such that the mass m remains stationary with respect to block of mass M, then the magnitude of the force P is

(M+m)gtanβ

gtanβ

mgcosβ

(M+m)gcosecβ