The maximum speed of a car on a road-turn of radius $30\, m$, if the coefficient of friction between the tyres and the road is $0.4$, will be .......... $m/sec$
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The maximum tension which an inextensible ring of mass $0.1\, kg/m$ can bear is $10\,N$. The maximum velocity in $m/s$ with which it can be rotated is ........ $m/s.$
Two blocks $A$ and $B$ of masses $5 \,kg$ and $3 \,kg$ respectively rest on a smooth horizontal surface with $B$ over $A$. The coefficient of friction between $A$ and $B$ is $0.5$. The maximum horizontal force (in $kg$ wt.) that can be applied to $A$, so that there will be motion of $A$ and $B$ without relative slipping, is
A cyclist riding the bicycle at a speed of $14 \sqrt{3} \,m / s$ takes a turn around a circular road of radius $20 \sqrt{3} \,m$ without skidding. What is his inclination to the vertical?
The maximum velocity (in $ms^{-1}$) with which a car driver must traverse a flat curve of radius $150 \,m$ and coefficient of friction $0.6$ to avoid skidding is
A motor car has a width $1.1$ m between wheels. Its centre of gravity is $0.62$ m above the ground and the coefficient of friction between the wheels and the road is $0.8$. ...... $m/s$ is the maximum possible speed, if the centre of gravity inscribes a circle of radius $15$ m ? (Road surface is horizontal)
A body of mass $'m '$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is $1\, cm$. If the angular velocity is doubled, the elongation in the spring is $5\, cm$. The original length of the spring is ......... $cm$
A bullet of mass $0.1\,kg$ moving horizontally with speed $400\,ms ^{-1}$ hits a wooden block of mass $3.9\,kg$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $20\,m$ before coming to rest. The coefficient of friction between the block and the surface is $........$ $\left(\text { Given } g=10 \,ms ^2\right. \text { ) }$
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