A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end. Show that whatever force the monkey exerts on the rope,the monkey and the block
Suppose the monkey acceleration upward with acceleration '$$a$$' & the block, acceleration downward with acceleration $$a_{1}$$. Let Force exerted by monkey is equal to $$T$$
From the free body diagram of monkey$$\therefore T-mg-ma=0$$
$$\Rightarrow T=mg+ma$$.Again from the FBD of the block
$$T=ma_{11}-mg=0$$
$$\Rightarrow T=mg+ma+ma_{1}-mg=0$$ [From (I)]
$$\Rightarrow ma=-ma_{1}\Rightarrow a=a_{1}$$
Acceleration $$-a$$ downward i.e. $$a$$ upward.
$$\therefore$$ The block & the monkey move in the same direction with equal acceleratio.If initially they are rest (no force is exertied by monkey) no motion of monkey of block occurs as they have same weight (same mass). Their separation will not changed as time passes.
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $$0.36\ kg$$ and $$0.72\ kg$$. Taking $$g = 10 m/s^{2}$$, find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.
Three equal weights of $$3 kg$$ each are hanging on a string passing over a frictionless pulley as shown in figure. The tension in the string between masses II and III will be (Take $$g=10m/sec^2$$):
Two masses $${M}_{1}=5kg$$ and $${M}_{2}=10kg$$ are connected at the ends of an inextensible string passing over a frictionless pulley as shown. When the masses are released, then the acceleration of the masses will be:
Both the string, shown in figure, are made of same material and have same cross-section. The pulleys are light. The wave speed of a transverse wave in the string AB is $$\upsilon _1$$ and in CD it is $$\upsilon _2$$. Then $$\upsilon _1 / \upsilon _2$$ is
The descending pulley shown in figure has a radius $$20\ cm$$ and moment of inertia $$0.20 kg-m^2$$. The fixed pulley is light and the horizontal plane frictionless. Find the acceleration of the block if its mass is $$1.0\ kg$$.
A table with smooth horizontal surface is placed in a cabin which moves in a circle of large radius R (figure 7-35) A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on the table are connected through a string going over the pulley. Initially the masses are held by a person with the strings along the ouward radius and then the system is released from rest Find the magnitude of the initial acceleration of the masses as seen from the cabin and the tension in the string
Calculate the tension in the string shown in figure. The pulley and the string are light and all surfaces are frictionless. Take $$g=10\ m/s^{2}$$.
Consider the situation shown in figure. Both the pulleys and the string are light and all the surfaces are frictionless. Find the acceleration of the mass M.
Find the acceleration of the block $$A$$ and $$B$$ in the three situation shown in figure.
In the arrangement shown in figure, the ends $$P$$ and $$Q$$ of an inextinsible string move downwards with uniform speed $$u$$. Pulleys $$A$$ and $$B$$ are fixed. The mass $$M$$ moves upwards with a speed