Question

A block of mass is placed on the top of a cart such that the time period of the system is assuming there is no slipping. If the cart is displaced by from its equilibrium position and released, then the coefficient of static friction between block and cart is just sufficient to prevent the block from sliding. The value of and respectively are (Take )

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

= 2.55 kg
Maximum acceleration of SHM is,
a_max = ω²A (A = amplitude)
i.e., maximum force on mass 'm' is m ω² A which is being provided by the force of friction between the mass and the cart. Therefore,

\mu_{ s } \geq \frac{\omega^{2} A }{ g }\mu_{ s } \geq\left(\frac{2 \pi}{ T }\right)^{2} \cdot \frac{ A }{ g }\mu_{ s } \geq\left(\frac{2 \pi}{0.75}\right)^{2}\left(\frac{0.05}{9.8}\right) \quad( A =50 mm )\mu_{ s } \geq 0.358\mu_{ s }