# Recent questions tagged theory-of-mechanics

A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of $10\:\text{grams}$, attached to four points on the $100\: mm$ ... the masses gets detached then the magnitude of the resultant unbalance force on the rotor is ________$N$ (rounded off to $2$ decimal places).
In the figure, link $2$ rotates with constant angular velocity $\omega_2$. A slider link $3$ moves outwards with a constant relative velocity $V_{Q/P}$, where $Q$ is a point on slider $3$ and $P$ is a point on link $2$. The magnitude and direction of Coriolis component of ... of $\omega_2$ $\omega_2$ $V_{Q/P}$; direction of $V_{Q/P}$ rotated by $90^\circ$ opposite to the direction of $\omega_2$
In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of $14$ $rad/s$ and the crank length is $300$ $mm$, the maximum acceleration of the slider (in $m$/$s^2$) is ___________
The initial velocity of an object is $40$ $m/s$. The acceleration a of the object is given by the following expression: $a=-0.1v$ where $v$ is the instantaneous velocity of the object. The velocity of the object after $3$ seconds will be _______
A small ball of mass $1$ $kg$ moving with a velocity of $12$ $m/s$ undergoes a direct central impact with a stationary ball of mass $2$ $kg$. The impact is perfectly elastic. The speed (in $m/s$) of $2$ $kg$ mass ball after the impact will be ____________
A point mass is executing simple harmonic motion with an amplitude of $10$ $mm$ and frequency of $4$ $Hz$. The maximum acceleration ($m/s^2$) of the mass is _______
A body of mass (M) $10$ $kg$ is initially stationary on a $45^{\circ}$ inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is $0.5$. The body slides down the plane and attains a velocity of $20 m/s$. The distance traveled (in meter) by the body along the plane is _______
A mass $m_1$ of $100$ $kg$ traveling with a uniform velocity of $5$ $m/s$ along a line collides with a stationary mass $m_2$ of $1000$ $kg$. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is $0.6$ $0.1$ $0.01$ $0$
A truck accelerates up a $10^0$ incline with a crate of $100$ $kg$. Value of static coefficient of friction between the crate and the truck surface is $0.3$. The maximum value of acceleration (in $m$/$s^2$) of the truck such that the crate does not slide down is _______
What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by $k_1$ and $k_2$ as shown below. $\sqrt{\dfrac{k_1+k_2}{2m}} \\$ $\sqrt{\dfrac{k_1+k_2}{4m}} \\$ $\sqrt{\dfrac{k_1-k_2}{m}} \\$ $\sqrt{\dfrac{k_1+k_2}{m}}$
A $4$-bar mechanism with all revolute pairs has link lengths $l_f$ = $20$ $mm$, $l_{\text{in}} = 40$ $mm$, $l_{\text{co}} =50$ $mm$ and $l_{\text{out}} =60$ $mm$. The suffixes $\text{ f'}$ ... can execute full circular motion Both links cannot execute full circular motion Only the output link cannot execute full circular motion Only the input link cannot execute full circular motion
A rigid link $PQ$ is $2$ $m$ long and oriented at $20^\circ$ to the horizontal as shown in the figure. The magnitude and direction of velocity $V_Q$, and the direction of velocity $V_P$ are given. the magnitude of $V_P$ (in $m/s$) a t this instant is $V_Q$=$1 m/s$ $2.14$ $1.89$ $1.21$ $0.96$