First slide

Application of Newtons laws

Question

Two wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to the block of mass M as shown in the figure. The magnitude of force P is

Moderate

A

$(M + m) g \tan β$
B

$g \tan β$
C

$m g \cos β$
D

$(M + m) g cosec β$

Solution

Acceleration of the system:
$a = \frac{P}{M + m} . . . . (i)$
The FBD of mass m is shown in the figure.
$\begin{array}{l} R \sin β = m a . . . . . . (i) \\ R \cos β = m g . . . . . (i i) \end{array}$
From Eqs. (ii) and (iii), we get
$a = g \tan β$
Putting the value of a in (i), we get
$P = (M + m) g \tan β$

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