# GATE Mechanical 2022 Set 2 | Question: 27

A rigid homogeneous uniform block of mass $1$ $\text{kg}$, height $h = 0.4 \:m$ and width $b = 0.3\: m$ is pinned at one corner and placed upright in a uniform gravitational field $(g = 9.81 m/s^{2})$, supported by a roller in the configuration shown in the figure. A short duration (impulsive) force $F$, producing an impulse $I_{F}$, is applied at a height of $d = 0.3\: m$ from the bottom as shown. Assume all joints to be frictionless. The minimum value of $I_{F}$ required to topple the block is

1. $0.953$ $\text{Ns}$
2. $1.403$ $\text{Ns}$
3. $0.814$ $\text{Ns}$
4. $1.172$ $\text{Ns}$
in Others
edited

## Related questions

$F(t)$ is a periodic square wave function as shown. It takes only two values, $4$ and $0$, and stays at each of these values for $1$ second before changing. What is the constant term in the Fourier series expansion of $F(t)$? $1$ $2$ $3$ $4$
Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point $(1, 2, 3)$. The surface integral $\int _{A} \vec{F}.d\vec{A}$ of a vector field $\vec{F} = 3x\hat{i} + 5y\hat{j} + 6z\hat{k}$ over the entire surface $A$ of the cube is _____________. $14$ $27$ $28$ $31$
Consider the definite integral $\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$ Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using Simpson’s rule with $10$ equal subintervals, the value is $I_{S}$. The percentage error is defined as $e = 100\times \left ( I_{e} - I_{S}\right )/I_{e}$. The value of $e$ is $2.5$ $3.5$ $1.2$ $0$
Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$ If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}} dx$ is _______________. $\sqrt{\pi a}$ $\sqrt{\frac{\pi }{a}}$ $b\sqrt{\pi a}$ $b\sqrt{\frac{\pi }{a}}$
A polynomial $\varphi \left ( s \right ) = a_{n}s^{n} + a_{n-1}s^{n-1} + \cdots + a_{1}s+a_{0}$ of degree $n>3$ with constant real coefficients $a_{n}, a_{n-1}, \:\dots a_{0}$ has triple roots at $s = -\sigma$ ... $\varphi \left ( s \right ) = 0,$ and $\frac{d^{3}\varphi \left ( s \right )}{ds^{3}} = 0$ at $s = -\sigma$