In a conical pendulum, the bob is rotated with different angular velocities and tension in the string is calculated for different values of $\omega$ . Which of them is correct graph between $T$ & $\omega .$
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A heavy box is to dragged along a rough horizontal floor. To do so, person $A$ pushes it at an angle $30^o$ from the horizontal and requires a minimum force $F_A$, while person $B$ pulls the box at an angle $60^o$ from the horizontal and needs minimum force $F_B$. If the coefficient of friction between the box and the floor is $\frac{{\sqrt 3 }}{5}$ , the ratio $\frac{{{F_A}}}{{{F_B}}}$ is
A $2 \mathrm{~kg}$ brick begins to slide over a surface which is inclined at an angle of $45^{\circ}$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:
A uniform rope of length l lies on a table. If the coefficient of friction is $\mu $, then the maximum length ${l_1}$ of the part of this rope which can overhang from the edge of the table without sliding down is
A car is moving on a horizontal circular road of radius $0.1 \,km$ with constant speed. If coefficient of friction between tyres of car and road is $0.4$, then speed of car may be ......... $m / s$ $\left(g=10 \,m / s ^2\right)$
A stone of mass $0.25\; kg$ tied to the end of a string is whirled round in a circle of radius $1.5 \;m$ with a speed of $40\; rev./min$ in a hortzontal plane. What is the tenston in the string? What is the maximum speed in $m/s $ with which the stone can be whirled around if the string can withstand a maximum tension of $200\; N ?$
A block is projected with speed $20 \,m / s$ on a rough horizontal surface. The coefficient of friction $(\mu)$ between the surfaces varies with time $(t)$ as shown in figure. The speed of body at the end of $4$ second will be ............ $m / s$ ( $g=$ $10 \,m / s ^2$ )
A block of mass $5\, kg$ is $(i)$ pushed in case $(A)$ and $(ii)$ pulled in case $(B)$, by a force $F = 20\, N$, making an angle of $30^o$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block, in case $(B)$ and case $(A)$ will be $....... ms^{-2}$ .$(g = 10\, ms^{-2})$