Question

why did Mahatma Gandhi feel the need to launcher broad-based Movement in 1920

Answer 1

The Non-Cooperation Movement was launched on 1st August 1920. 
These were the factors that made Gandhi feel the need to launch a broad based movement in 1920:

1. The Rowlett Act of 1919 stated that government could detain any political prisoner without any trials for 2 years. This was to stop the political activities of nationalists. 

2. The Jallianwala Bagh massacre of 1919: Under the command of Brigadier-General Reginald Dyer, 90 soldiers fired the people. The only exit had been blocked. Some 369 protesters were killed and over thousands of other people injured which also included children. 
Obviously after the incident, Gandhi lost any faith he had left in the British and declared it to be 'sin' to cooperate with them. One of the reasons for the movement was to avenge the injustice metted out to the victims. 

3. Other reasons included economic hardships of the common man especially farmers and decline in Indian artisans because all handmade goods were being replaced by the British ones. 
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Most of the activities were non-violent like boycotting the use of British products and their educational institutions, not going to work at the factories or farms, peaceful strikes and shouting of slogans. 
However, the movement did gradually grow violent (the Chauri Chaura incident) and Gandhi decided to withdraw the movement. 

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Answer 2

Mahatma Gandhi returned to India from South Africa in 1915. In South Africa, he had successfully fought the racist regime with a novel method known as Satyagraha.
The three reasons stating the fact are
(i) The idea of Satyagraha emphasized the power of truth which would ultimately triumph; Gandhiji believed that the dharma of non-violence could unite all Indians.
In India, Gandhiji launched Satyagraha movements in various areas like Champaran, Kheda, and Ahmedabad.
(ii) In 1919, the Rowlatt Act was passed by the Imperial Legislative Assembly which gave enormous power to the British Government.
The government could detain any political prisoner without any trial for two years. The aim of this Act was to repress political activities of the nationalists. People were agitating against the law.
(iii) On 13th April 1919, the infamous incident took place where hundreds of innocent people were killed. As the news of Jallianwalla Bagh spread, a widespread movement started.
Gandhiji now felt the need to launch a more broad-based movement in India.