Question

A block of mass m slides in an inclined right angled trough as shown in the figure. If the coefficients of kinetic friction between block and material composing the trough is m_k, find the acceleration of the block –

• A. g(sin q – $\sqrt { 2 } \mu _ { \mathrm { k } }$ cosq)
• B. g(sin q –m_kcosq)
• C. g(sin q –2m_kcosq)
• D. g(sin q – $\sqrt { \mu } _ { \mathrm { k } }$ cosq)

Answer 1

Answer: (A)

g(sin q – $\sqrt { 2 } \mu _ { \mathrm { k } }$ cosq)

Answer 2

Normal reaction of each surface,

$\frac { \mathrm { N } } { \sqrt { 2 } } + \frac { \mathrm { N } } { \sqrt { 2 } }$ = mg cosq ̃ N = $\frac { \mathrm { mg } } { \sqrt { 2 } }$ cosq ..(1)

̃ mg sinq – (mN + mN) = ma

̃ a = g sin q – $\sqrt { 2 }$ mg cosq