A particle is projected with a speed ${v_0} = \sqrt {gR} $ . The coefficient of friction between the particle and the hemispherical plane is $\mu = 0.5$ . Then, the initial acceleration of the particle is
Medium
Download our app for free and get started
$\mathrm{N}-\mathrm{mg}=\frac{\mathrm{mv}^{2}}{\mathrm{R}}=\mathrm{mg}$
$\mathrm{f}_{\mathrm{k}}=\mu \mathrm{N}$
$\mathrm{f}_{\mathrm{k}}=2 \mu \mathrm{mg}$
$\mathrm{ma}_{\mathrm{T}}=2 \mu \mathrm{mg}$
$a_{T}=2 \mu g(\leftarrow)$
$\mathrm{a}_{\mathrm{N}}=\frac{\mathrm{v}^{2}}{\mathrm{R}}=(\uparrow)$
$a=\sqrt{a_T^2+a_N^2}$
$a=\sqrt{2} g$ $ \nwarrow $
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A body $B$ lies on a smooth horizontal table and another body $A$ is placed on $B$. The coefficient of friction between $A$ and $B$ is $\mu $. What acceleration given to $B$ will cause slipping to occur between $A$ and $B$View Solution
- 2$A$ particle inside the rough surface of $a$ rotating cone about its axis is at rest relative to it at $a$ height of $1m$ above its vertex. Friction coefficient is $\mu = 0.5$, if half angle of cone is $45^o$, the maximum angular velocity of revolution of cone can be :View Solution
- 3As shown in the figure, two strings of length $l$ each are attached with a vertical axis $AB$ of length $l$. Strings are $AC$ and $BC$. At point $C$ a point mass m is attached. Mass rotates about axis with angular velocity. Tensions in $AB$ and $BC$ are $T_1$ and $T_2$ respectively. Choose the $CORRECT$ alternative :-View Solution
- 4View SolutionA car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud, as it leaves the ground are thrown
- 5View SolutionWhich of the following is correct, when a person walks on a rough surface
- 6Initially the whole system is at rest and now a force of $62\ N$ is applied on the block $B$ as shown in the figure. Find the time taken by $'A'$ to fall from the block $'B'$ ........... $\sec$View Solution
- 7Given in the figure are two blocks $A$ and $B$ of weight $20\ N$ and $100\ N,$ respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$, the frictional force applied by the wall on block $B$ is ........... $N$View Solution
- 8A small block starts slipping down from a point $B$ on an inclined plane $A B,$ which is making an angle $\theta$ with the horizontal section $BC$ is smooth and the remaining section $CA$ is rough with a coefficient of friction $\mu .$ It is found that the block comes to rest as it reaches the bottom (point $A)$ of the inclined plane. If $B C=2A C$, the coefficient of friction is given by $\mu=k \tan \theta$ .The value of $k$ isView Solution
- 9A vehicle of mass $200\,kg$ is moving along a levelled curved road of radius $70\,m$ with angular velocity of $0.2\,rad / s$. The centripetal force acting on the vehicle is $.........\,N$View Solution
- 10Two masses $M$ and $m$ are attached to a vertical axis by weightless threads of combined length $l$. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity $\omega $. If the tensions in the threads are the same during motion, the distance of $M$ from the axis isView Solution